User’s Manual Time Series Modelling Version 4.43 James Davidson

Transcription

Time Series Modelling Version 4.43
User’s Manual
James Davidson
19th July 2014
This document is also accessible through the program Help pages.
There is no conventional index since the text is revised regularly. The PDF file with
the Search option in Acrobat Reader provide an effective indexing capability.
Contents
0. Introduction ............................................................................................................ 8 0.1 TSM Basics ...................................................................................................... 8 1. ENTERING DATA ................................................................................................................ 8 2. MENUS AND DIALOGS. ..................................................................................................... 8 3. COMPUTING ESTIMATES, TESTS AND FORECASTS .................................................. 8 4. SAVING PROGRAM SETTINGS ........................................................................................ 9 5. ORGANIZING YOUR WORK ............................................................................................. 9 6. SIMULATION ....................................................................................................................... 9 7. MODELS ............................................................................................................................... 9 8. PROGRAMMING WITH TSM ........................................................................................... 10 9. TYPES OF MODEL ............................................................................................................ 10 10. SELECTING VARIABLES ............................................................................................... 10 11. VARIABLE "TYPES" ...................................................................................................... 11 12. PARAMETER VALUES ................................................................................................... 11 13. CODED FUNCTIONS....................................................................................................... 11 14. SYSTEMS OF EQUATIONS ............................................................................................ 12 15. OUTPUT CONVENTIONS ............................................................................................... 12 0.2 How To .... .................................................................................................... 13 1. HOW TO LOAD A DATA SET .......................................................................................... 13 2. HOW TO PLOT DATA SERIES......................................................................................... 13 3. HOW TO RUN A SIMPLE REGRESSION. ....................................................................... 13 4. HOW TO GENERATE QUARTERLY DUMMIES ........................................................... 14 5. HOW TO TAKE LOGARITHMS OF YOUR DATA ......................................................... 14 6. HOW TO TEST THE SIGNIFICANCE OF THE REGRESSION ...................................... 14 7. HOW TO TEST FOR A UNIT ROOT ................................................................................ 14 8. HOW TO ESTIMATE AN ARMA(p,q) MODEL ............................................................... 14 9. HOW TO FORECAST WITH AN ARMA/ARIMA MODEL ............................................ 15 10. HOW TO ESTIMATE A SIMPLE VAR MODEL ............................................................ 15 11. HOW TO ESTIMATE A GARCH MODEL ..................................................................... 16 1. User Interface ....................................................................................................... 17 1.1 The Menus ..................................................................................................... 17 1.2 Status Bar and Tool Bar ................................................................................. 18 1.3 The Results Window ...................................................................................... 19 1.4 Dialogs ........................................................................................................... 21 1.5 Entering Formulae ......................................................................................... 22 TYPING FORMULAE ............................................................................................................ 22 RESERVED NAMES .............................................................................................................. 24 1.6 File Drag-and-Drop........................................................................................ 25 2. File ....................................................................................................................... 27 2.0 File: General Information .............................................................................. 27 MRU LISTS ............................................................................................................................. 28 FILE DIALOG ......................................................................................................................... 28 1
© James Davidson 2014
RESTART ................................................................................................................................ 28 2.1 File / Settings ................................................................................................. 29 IMPORTING MODELS .......................................................................................................... 30 EXPORTING SETTINGS ....................................................................................................... 31 SETTINGS AS TEXT.............................................................................................................. 31 2.2 File / Data....................................................................................................... 32 DATA DESCRIPTIONS ......................................................................................................... 33 MISSING OBSERVATIONS .................................................................................................. 33 PERIODIC OBSERVATIONS AND DATES ......................................................................... 34 PERIODIC DATES ................................................................................................................. 34 CALENDAR DATES .............................................................................................................. 35 DATE LABELS ....................................................................................................................... 35 PANEL DATA ......................................................................................................................... 35 SPREADSHEET EDITING ..................................................................................................... 37 TROUBLESHOOTING ........................................................................................................... 38 2.3 File / Results .................................................................................................. 38 2.4 File / Listings ................................................................................................. 39 LISTING FILES....................................................................................................................... 39 SPREADSHEETS .................................................................................................................... 40 2.5 File / Tabulations ........................................................................................... 41 2.6 File / Graphics ................................................................................................ 42 2.7 File / Folders .................................................................................................. 42 3. Setup .................................................................................................................... 44 3.1 Setup / Set Sample ........................................................................................ 44 3.2 Setup / Data Sets ............................................................................................ 45 3.3 Setup / Data Transformations and Editing ..................................................... 47 EDIT COMMANDS ................................................................................................................ 47 TRANSFORM COMMANDS ................................................................................................. 51 3.4 Setup / Data Spreadsheet ............................................................................... 53 WINDOWS IMPLEMENTATION ......................................................................................... 53 LINUX/AWTJAPI IMPLEMENTATION............................................................................... 54 3.5 Setup / Make Data Formula ........................................................................... 55 TEXT BOX CONTROLS ........................................................................................................ 56 3.6 Setup / Automatic Model Selection ............................................................... 56 AUTOMATIC REGRESSOR SELECTION ........................................................................... 56 MULTIPLE ARMA MODELS ................................................................................................ 57 3.7 Setup / Recursive/Rolling Estimation ............................................................ 57 3.8 Setup / Compute Summary Statistics............................................................. 58 3.9 Setup / Nonparametric Regression ................................................................ 60 3.10 Setup / Semiparametric Long Memory ........................................................ 60 3.11 Setup / Cointegration Analysis .................................................................... 61 3.12 Setup / Monte Carlo Experiments... ............................................................. 62 OPTIONS:................................................................................................................................ 64 OUTPUTS ................................................................................................................................ 66 RUNNING AN EXTERNAL PROCESS ................................................................................ 67 CONDOR ................................................................................................................................. 67 PARALLEL PROCESSING .................................................................................................... 68 WARP SPEED BOOTSTRAP ................................................................................................. 69 3.13 Setup / Tail Probabilities and Critical Values... .......................................... 69 3.14 SsfPack State Space Modelling .................................................................. 70 MODEL COMPONENTS........................................................................................................ 71 MODEL DIMENSIONS .......................................................................................................... 72 MATRIX EDITING ................................................................................................................. 72 TASKS ..................................................................................................................................... 73 4. Model ................................................................................................................... 76 4.0 Model / General ............................................................................................. 76 2
MODEL MANAGER .............................................................................................................. 76 BUTTONS ............................................................................................................................... 76 ACTIVATING SPECIAL FEATURES ................................................................................... 77 DIALOG CONTROL............................................................................................................... 77 SPECIFYING SYSTEMS OF EQUATIONS .......................................................................... 77 AUTOMATIC DATA TRANSFORMATION ........................................................................ 78 CONDITIONAL VARIANCE SIMULATION ....................................................................... 79 4.1 Model / Model Manager ................................................................................ 79 STORING MODELS ............................................................................................................... 80 LOADING MODELS .............................................................................................................. 81 DEFAULTS ............................................................................................................................. 82 MODEL DESCRIPTIONS ...................................................................................................... 82 DELETING MODELS............................................................................................................. 82 4.2 Model / Linear Regression... .......................................................................... 82 VARIABLE AND LAG SPECIFICATION ............................................................................ 84 WALD TEST OF CONSTRAINTS ......................................................................................... 85 COINTEGRATING REGRESSION........................................................................................ 85 4.3 Model / Panel Data... ..................................................................................... 86 DATA TRANSFORMATIONS ............................................................................................... 86 DUMMY VARIABLES........................................................................................................... 86 ESTIMATOR ........................................................................................................................... 87 TESTS AND DIAGNOSTICS ................................................................................................. 87 4.4 Model / Dynamic Equation... ......................................................................... 88 ESTIMATION CRITERIA ...................................................................................................... 89 MODEL SPECIFICATION ..................................................................................................... 90 VARIABLE SELECTION ....................................................................................................... 90 LINEAR REGRESSION ......................................................................................................... 91 BILINEAR MODEL ................................................................................................................ 91 NONLINEAR MOVING AVERAGE (SPS) ........................................................................... 91 OTHER MODEL FEATURES ................................................................................................ 92 SYSTEMS OF EQUATIONS .................................................................................................. 92 ESTIMATING TYPE I (V)ARFIMA PROCESSES ............................................................... 93 4.5 Model / Conditional Variance........................................................................ 94 MULTIVARIATE GARCH ..................................................................................................... 95 4.6 Model / Coded Function... ............................................................................. 95 METHODS .............................................................................................................................. 96 INTERACTIVE CODING ....................................................................................................... 96 TYPES OF FORMULAE ........................................................................................................ 97 TEXT BOX CONTROLS ........................................................................................................ 99 PARSING THE MODEL ......................................................................................................... 99 PARAMETER NAMES........................................................................................................... 99 VARIABLE NAMES............................................................................................................... 99 SIMULATING CODED EQUATIONS ................................................................................ 100 SIMULATING WITH RANDOM EXPLANATORY VARIABLES ................................... 100 OX CODING ......................................................................................................................... 101 4.7 Model / Regime Switching... ....................................................................... 102 MARKOV SWITCHING....................................................................................................... 103 EXPLAINED SWITCHING .................................................................................................. 103 SMOOTH TRANSITION ...................................................................................................... 104 4.8 Model / Equilibrium Relations... ................................................................. 104 4.9 Model / Parameter Constraints... ................................................................. 107 REGRESSOR SIGNIFICANCE TEST.................................................................................. 107 CODED_RESTRICTIONS .................................................................................................... 108 4.10 Model / Select Instruments... ..................................................................... 109 5. Values ................................................................................................................ 111 5.0 Values: General............................................................................................ 111 BUTTONS ............................................................................................................................. 111 VALUES FIELDS ................................................................................................................. 112 FIXED PARAMETERS......................................................................................................... 112 3
PARAMETER BOUNDS ...................................................................................................... 112 GRID PLOTS ......................................................................................................................... 112 WALD TESTS AND LINEAR RESTRICTIONS ................................................................. 113 5.1 Values / Equation... ...................................................................................... 113 5.2 Values / Equilibrium Relations... ................................................................. 114 5.3 Values / Distribution... ................................................................................. 114 5.4 Values / Switching Regimes... ..................................................................... 114 6. Actions ............................................................................................................... 116 6.1 Actions / Run Estimation ............................................................................. 116 BATCH JOBS ........................................................................................................................ 116 6.2 Actions / Evaluate at Current Values ........................................................... 116 6.3 Actions / Estimate Multiple ARMA Models ............................................... 116 6.4 Actions / Automatic Regressor Selection .................................................... 117 6.5 Actions / Recursive/Rolling Estimation ...................................................... 118 6.6 Actions / Plot Criterion Grid ........................................................................ 119 6.7 Actions / Multi-Stage GMM ........................................................................ 120 6.8 Actions / Compute Test Statistic ................................................................. 120 SCORE (LM) TEST ............................................................................................................... 121 MOMENT (M or CM) TEST ................................................................................................. 121 LM TESTS OF PARAMETER RESTRICTIONS ................................................................. 122 WALD TEST OF SET RESTRICTIONS .............................................................................. 122 SPECIFIED DIAGNOSTIC TESTS ...................................................................................... 122 TEST FOR I(0) DEPENDENT VARIABLE ......................................................................... 122 6.9 Actions / Compute Forecasts & IRs ............................................................ 123 6.10 Actions / Retrieve Series............................................................................ 123 6.11 Actions / Simulate Current Model ............................................................. 124 PANEL DATA ....................................................................................................................... 125 6.12 Other Commands ....................................................................................... 125 SET DEFAULT VALUES ..................................................................................................... 125 CLEAR VALUES .................................................................................................................. 125 CLEAR RESULTS WINDOW .............................................................................................. 125 CLOSE ALL DIALOGS ........................................................................................................ 125 RESTORE DIALOGS ........................................................................................................... 125 RESET DIALOG POSITIONS .............................................................................................. 125 7. Graphics ............................................................................................................. 127 7.0 Graphics: General Information ................................................................... 127 7.1 Graphics / Show Data Graphic .................................................................... 127 SIMPLE PLOTTING ............................................................................................................. 127 MULTI_SERIES PLOTTING ............................................................................................... 129 7.2 Graphics / Equation Graphics ...................................................................... 130 7.3 Graphics / Monte Carlo Graphics ................................................................ 131 8. Options ............................................................................................................... 134 8.0 Options: General Information and Defaults................................................. 134 8.1 Options / Output and Retrievals .................................................................. 136 SAVING DATA FILES ......................................................................................................... 136 EXPORTING AND PRINTING LISTINGS ......................................................................... 136 EXPORTING GRAPHICS .................................................................................................... 137 OUTPUTTING TABLES ...................................................................................................... 137 OUTPUTTING SERIES ........................................................................................................ 138 RETRIEVING GENERATED SERIES ................................................................................. 138 8.2 Options / Tests and Diagnostics .................................................................. 138 CORRELOGRAM POINTS .................................................................................................. 138 LM TESTS OF SET RESTRICTIONS AND "FIXED" VALUES........................................ 139 FORM OF THE LM STATISTICS........................................................................................ 139 LAGS FOR THE ADF AND ERS TESTS OF I(1) ............................................................... 139 DIAGNOSTIC TESTS........................................................................................................... 140 4
COVARIANCE MATRIX FORMULAE .............................................................................. 140 HAC KERNEL FORMULAE AND BANDWIDTH ............................................................. 140 MODEL SELECTION CRITERIA........................................................................................ 141 SUPPLYING AN EDF FILE FOR P-VALUES .................................................................... 141 8.2a Options / Tests and Diagnostics / Diagnostic Tests... ................................ 142 Q TESTS FOR SERIAL DEPENDENCE ............................................................................. 142 SCORE (LM) TESTS ............................................................................................................ 142 CONDITIONAL MOMENT (CM) TESTS ........................................................................... 143 RESIDUAL-BASED TESTS ................................................................................................. 144 OTHER DIAGNOSTIC TESTS ............................................................................................ 144 CONSISTENT SPECIFICATION TESTS ............................................................................ 145 8.3 Options / Forecasting ... .............................................................................. 147 FORECASTS ......................................................................................................................... 147 FORECAST TYPE ................................................................................................................ 147 MULTI_STEP FORECAST METHOD ................................................................................ 148 MONTE CARLO SETTINGS ............................................................................................... 149 ACTUALS IN FORECAST PLOT ........................................................................................ 149 STANDARD ERRORS AND CONFIDENCE BANDS ...................................................... 149 FORECAST ERROR VARIANCE DECOMPOSITION ...................................................... 149 PLOT DISPLAY .................................................................................................................... 150 IMPULSE RESPONSES ....................................................................................................... 150 8.4 Options / Simulation and Resampling ... ..................................................... 150 SIMULATION OPTIONS ..................................................................................................... 150 SIMULATION PRESAMPLE MODE .................................................................................. 152 RANDOM NUMBER GENERATION ................................................................................. 153 INFERENCE BY RESAMPLING ......................................................................................... 153 RESAMPLING CONFIDENCE INTERVALS ..................................................................... 154 NEWTON-RAPHSON ALGORITHM .................................................................................. 155 TYPE I FRACTIONAL PROCESSES .................................................................................. 155 8.5 Options / Graphics ... ................................................................................... 156 TEXT ATTRIBUTES ............................................................................................................ 156 BITMAP DIMENSIONS ....................................................................................................... 156 DATES IN PLOTS ................................................................................................................ 156 OTHER PLOTTING OPTIONS ............................................................................................ 157 CONFIDENCE BANDS ........................................................................................................ 157 MULTIPLE SERIES DISPLAY ............................................................................................ 158 LEGENDS ............................................................................................................................. 158 3-D PLOTS ............................................................................................................................ 158 DISTRIBUTION PLOTS....................................................................................................... 159 8.5a Options / Graphics / Lines and Symbols ................................................... 159 LINE AND SYMBOL STYLES ............................................................................................ 159 SCATTER_PLOT OPTIONS ................................................................................................ 160 8.6 Options / ML and Dynamics ... .................................................................... 161 ML PARAMETERIZATION ................................................................................................ 161 DYNAMIC MODEL SETTINGS .......................................................................................... 161 GARCH PARAMETERIZATION......................................................................................... 162 OPTIMIZATION SETTINGS ............................................................................................... 163 8.7 Options / Optimization and Run ... .............................................................. 163 OPTIMIZATION SETTINGS: BROYDEN-FLETCHER- .................................................. 163 GOLDFARB-SHANNO (BFGS) ALGORITHM .................................................................. 163 SIMULATED ANNEALING ................................................................................................ 164 OPTIMAND CONVENTION................................................................................................ 164 NUMBER OF GRID POINTS ............................................................................................... 164 SUPPRESSING THE OUTPUT ............................................................................................ 164 RUNNING AN EXTERNAL PROCESS .............................................................................. 165 RUNNING A CONDOR JOB................................................................................................ 165 8.8 Options / General Options ... ....................................................................... 165 INTERFACE SETTINGS ...................................................................................................... 165 OPERATIONAL SETTINGS ................................................................................................ 167 5
LINEAR REGRESSION MODE ........................................................................................... 167 DEFER EXTERNAL JOBS ................................................................................................... 167 LOAD MULTIPLE DATA SETS.......................................................................................... 168 ASSIGNABLE TOOLBAR BUTTONS ................................................................................ 168 SPECIAL SETTINGS ............................................................................................................ 168 9. Help .................................................................................................................... 171 USER'S MANUAL ................................................................................................................ 171 VIEW TEXT FILES .............................................................................................................. 171 DESCRIPTIONS.................................................................................................................... 171 REGISTRATION................................................................................................................... 172 10. Interpreting the Output ..................................................................................... 173 PARAMETER LABELLING ................................................................................................ 173 PARAMETER ROOT TRANSFORMATIONS .................................................................... 173 STANDARD ERRORS, TEST STATISTICS AND P-VALUES ........................................ 174 SELECTION CRITERIA AND SUMMARY STATISTICS................................................. 174 CONVERGENCE ISSUES .................................................................................................... 175 GRAPHICS FOR REGIME SWITCHING MODELS .......................................................... 175 BOOTSTRAP AND SUBSAMPLING P-VALUES.............................................................. 176 11 Directories and Files ......................................................................................... 177 DIRECTORIES (Windows folders): ...................................................................................... 177 FILES ..................................................................................................................................... 177 FILE TYPES .......................................................................................................................... 178 12. Hints and Tips .................................................................................................. 180 NUMERICAL OPTIMIZATION .......................................................................................... 180 CHOICE OF SYSTEM ESTIMATORS ................................................................................ 181 USING THE RESULTS WINDOW AS A TEXT EDITOR ................................................. 182 ENTERING DATA BY HAND ............................................................................................. 182 MAINTAINING AND EXPORTING PROGRAM SETTINGS ........................................... 183 DOING SIMULATIONS ....................................................................................................... 184 STARTING TSM FROM WINDOWS EXPLORER ............................................................ 185 RUNNING SEVERAL INSTANCES OF TSM .................................................................... 185 TROUBLESHOOTING ......................................................................................................... 186 What's New? .......................................................................................................... 188 TSM 4.37 ........................................................................................................... 188 TSM 4.36 ........................................................................................................... 189 TSM 4.35 ........................................................................................................... 189 TSM 4.34 ........................................................................................................... 189 TSM 4.33 ........................................................................................................... 189 TSM 4.32 ........................................................................................................... 189 TSM 4.31 ........................................................................................................... 189 TSM 4.30 ........................................................................................................... 189 TSM 4.29 ........................................................................................................... 190 TSM 4.28 ........................................................................................................... 190 TSM 4.27 ........................................................................................................... 190 TSM 4.26 ........................................................................................................... 190 TSM 4.25 ........................................................................................................... 190 TSM 4.24 ........................................................................................................... 190 TSM 4.23 ........................................................................................................... 191 TSM 4.22 ........................................................................................................... 191 TSM 4.21 ........................................................................................................... 191 TSM 4.20 ........................................................................................................... 191 TSM 4.19 ........................................................................................................... 191 TSM 4.18 ........................................................................................................... 192 TSM 4.17 ........................................................................................................... 192 TSM 4.16 ........................................................................................................... 192 6
TSM 4.15 ........................................................................................................... 192 7
0. Introduction
0.1 TSM Basics
TIME SERIES MODELLING Version 4 is an interactive package for modelling and
forecasting time series. It is designed primarily for nonlinear dynamic model
estimation, including ARMA and ARFIMA models, conditional variance models
(ARCH/GARCH and several variants), regime-switching and smooth transition.
It also functions well as a user-friendly, general purpose regression package.
To enhance its power and ease of use, the program has various special features not
found in comparable packages. It is strongly recommended to read through this
introduction before starting work with TSM. It does not aim to describe all the
capabilities of the package. These can best be discovered by browsing the menus
in conjunction with the Help pages provided for each. Its purpose is to outline
TSM's unique design and operating conventions to first-time users.
****************
Working with TSM
****************
1. ENTERING DATA
Regression packages often have their own proprietary database formats, and getting
data into them from different sources can be troublesome. By contrast, TSM reads
either ASCII files or spreadsheet files directly. It works smoothly in conjunction
with popular spreadsheet programs such as Microsoft Excel, and also OxMetrics.. It
can itself merge datasets with different start and finish dates and use
and display date information, including daily dates in Excel format. It offers flexible
single-observation editing, series transformations, and dummy creation capabilities.
2. MENUS AND DIALOGS.
TSM is operated in Graphical User Interface (GUI) mode by setting the options in
a number of dialogs. These can be opened from the menu bar or by shortcut buttons
on the tool bar. Some operations can be performed in several different ways. For
example, an estimation run can be launched from the menus, from the "Running
Man" toolbar button, and also from the "Go" buttons in several dialogs. The action
of the toolbar button can vary depending on the dialog currently open.
3. COMPUTING ESTIMATES, TESTS AND FORECASTS
The basic method of operation is as follows:
1)
Specify the calculations and settings desired, using the Setup, Model,
Values and Options menus.
2)
Launch the estimation module using one of the commands on the Actions
menu, a dialog button, or a tool bar button.
Both the "Running Man" and the "Calculator" buttons on the tool bar launch closed
form (non-iterative) estimations, such as OLS and IV, and associated tests and
forecasts. For nonlinear estimation (if enabled) the "Running Man" button launches
the optimization algorithm, while the "Calculator" button just performs postestimation computations (forecasts or tests) using the currently stored parameter
values, either obtained on the latest run or entered by the user.
NOTE: forecasts and tests are not computed by merely specifying them in the
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Options dialog! Use the menu items in the Actions menu for this purpose. The
Calculate button performs all the currently specified calculations and generates the
complete estimation output for the current parameter values.
Each run has a unique ID number to identify the outputs associated with it, such as
graphics files, spreadsheet files, and settings files.
4. SAVING PROGRAM SETTINGS
TSM has a large number of optional settings that most users will want to change
only occasionally. By default, the program automatically saves at shutdown all
current settings in a special file called "settings.tsm". When the program is
restarted the working environment, with all selected options, is then exactly as
it was in the last session. Named settings files (with .tsm extension and 'red TSM'
Windows icon) can be saved and re-loaded manually at any time.
5. ORGANIZING YOUR WORK
The File / Settings / Export... command saves a complete image of the current
session, including options, model specifications, data, generated series, tables and
graphics. 'Exported' .tsm files do not contain local path information and are fully
portable between installations. When they are opened, the data file and temporary
storage (.tsd) files are recreated. This provides an ideal way to share work with
collaborators, move between home/office installations and distribute classroom
exercises. Double-clicking on a .tsm file icon in Windows Explorer starts the
program and loads the file contents automatically.
6. SIMULATION
Part of the TSM philosophy is that any model that can be estimated by the program
can also be simulated, using randomly generated disturbances or bootstrapped
(randomly resampled) residuals. The former can be Gaussian, or generated from the
distribution specified by the selected likelihood function. This feature can be used for
one-off simulations whose output is graphed. Comparing the simulation of the fitted
model with the original data can be a useful informal diagnostic tool. However, the
main application for the simulation module is to running bootstrap tests and Monte
Carlo experiments. A flexible interactive Monte Carlo module is provided.
7. MODELS
A "model" is a complete set of specifications and values to estimate, simulate or
forecast an equation or system of equations. Any number of these specifications
can be stored and recalled during a session, as well as saved permanently in the
settings (.tsm) file. For example, this option allows the user to run an exploratory
regression on the fly, while working on a complex multiple-equation model,
without losing any settings and values. Just use the Model Manager to store the
current settings and values to a named model (optionally including the data set).
Load the model to restore them again. The generated series, graphics and
(optionally) data set associated with a model are stored in a file with '.tsd'
extension and 'blue TSM' Windows icon
Models are also used for running Monte Carlo experiments. Select one model
to generate the data using the simulation module, and another (or the same)
model for estimating, allowing a very flexible approach to misspecification
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analysis.
8. PROGRAMMING WITH TSM
TSM can be called as a module in your own Ox program. It is easy to
write out the commands and options set by TSM dialogs as lines of Ox code.
Your program can call the main program functions such as "Run_Estimation"
and "Run_Simulation", and perform further operations on the output.
The special scripting language is fully detailed in the programming manual. To see
what your current set of (non-default) options looks like in coded form, give the
command File / Settings / Display/Save Text... and inspect the listing created.
The reverse operation is also possible. Write out a set of coded commands in
the TSM launch file, and these options are then set when the GUI program is
started. This provides an alternative way to set and maintain your list of
favourite program options.
*****************
Modelling with TSM
*****************
9. TYPES OF MODEL
There are two main model specification dialogs, called respectively Linear
Regression and Dynamic Equation. The "regression scatter" and "space shuttle"
toolbar buttons give direct access to these. (The latter can be optionally hidden
to simplify the interface, if these features are not being used.)
Linear Regression is used to specify linear models for estimation by a closedform expression (or, at most, a fixed, finite sequence of calculations). These
include OLS, 2SLS, SUR and 3SLS.
Although linear regressions can also be specified in the Dynamic Equation dialog,
its special role is to set up nonlinear dynamic models. All estimation in this dialog,
even of linear models, is done by optimizing a log-likelihood or other criterion
function numerically, using the BFGS and/or simulated annealing algorithms.
Model choices include Gaussian, Student t and GED continuous distributions,
binary logit and probit models, and count data models. All these models can
feature conditional variances, and Markov switching or smooth transition
nonlinearity.
10. SELECTING VARIABLES
Model specification dialogs include a list of variable names, corresponding to the
currently loaded data file. Selecting a variable is a two-step procedure. First select a
radio button specifying the variable Type - dependent variable(s), one of several
types of explanatory variables, instruments, and so forth. Next, click on the desired
name in the list, to highlight it. The list can be scrolled, if it is too long to display
complete in the dialog. Note that when one or more variables are selected in a
category, the corresponding radio button is highlighted with a lighter-grey panel.
To see which variables are currently selected in a particular category, click on the
radio button in question. A little practice helps to get variable selection smooth and
rapid, and it is a good idea to click on each highlighted button in turn to check the
specification is as desired, before launching the estimation run. To deselect a
variable, simply click on it again to remove the highlight. There is also a "Clear"
button to remove all the current selections.
NOTE: to display time plots of one or more variables, highlight them in the list
10
and click the 'Data Graphics' button on the toolbar
11. VARIABLE "TYPES"
Explanatory variables in an equation can be of two, or three, different "Types", with
a different radio button assigned to each. In some models "typing" is irrelevant
(in which case, just choose Type 1), but it has a number of common uses. In linear
regressions, it is used to allow lags to be treated differently. Lags up to a specified
order can be included automatically, so that lagged values do not need to be created
and stored individually in the database. The number of lags is selected with the scroll
bar, for all variables of the given Type. For example, assign non-lagged variables
such as dummies to Type 1, and distributed lag regressors to Type 2. To allow easy
inclusion of the lagged dependent variable, the dependent variable in a regression
can be assigned as a Type 2 regressor with lags specified. The current value is
omitted from the regressor set automatically. This also works in system models such
as VARs.
In the Dynamic Equation dialog, "typing" regressors in combination with specifying
autoregressive and moving average components has a special additional role,
allowing an equation to feature "structural dynamics" and/or "error dynamics". See
the relevant Help pages and the TSM main document, for details on this.
12. PARAMETER VALUES
A special feature of TSM is the Values dialogs, where values and conditions for
model parameters can be set. Among the uses of these dialogs are
*
Setting starting values for numerical optimization
*
Fixing parameters at chosen values during estimation
*
Setting inequality constraints on parameters during estimation
*
Setting zero or linear restrictions on parameters, either for constrained
estimation, or calculation of Wald tests.
The Values dialogs can be accessed from the menu bar, or by the "Values" button in
the relevant model specification dialog.
Parameter values obtained in the latest estimation run can be viewed in the Values
dialogs, and will form the starting values for the next run unless edited or cleared.
Alternatively, the menu item Evaluate at Current Values (or the "Calculator"
button) generates the program outputs at these values, without re-optimizing.
13. CODED FUNCTIONS
General nonlinear models can be estimated by creating coded formulae. The
program features a formula parser which can evaluate functions of data and/or
parameters typed using standard notations. This feature is used to create
functions for estimation and parameter restrictions for testing, as well as data
transformations.
Alternatively, TSM can estimate a model programmed by the user in the Ox
language, while making use of all the estimation, testing and forecasting features
of the package. (This feature is distinct from, though compatible with, calling
TSM from within an Ox program.)
11
14. SYSTEMS OF EQUATIONS
Setting up a system of equations is greatly simplified by requiring that the righthand side of every equation has the same specification. In this way, only one
specification has to be created and stored. This is the natural approach for an
unrestricted VAR, for example. To have the equations different from each other
(e.g. with identifying restrictions imposed) the method is to create an inclusive
specification of which all the actual equations are special cases, and then "fix" the
surplus parameters at zero in the Values dialogs - enter 0 in the value fields, and
check the 'Fixed' checkboxes. While editing values, one can switch easily from
one equation to another, using the 'Next Equation' button or the choice widget
on the tool bar. Parameters fixed at 0 are not reported in the output, although
those fixed at non-zero values are listed as such.
Systems of coded nonlinear functions can be estimated in the same way. While
their specifications can differ, each has the common set of named parameters
assigned to it - "fix" the surplus ones in Values / Equation, so that the search
algorithm ignores them.
Simultaneous equation systems can be specified by including variables as both
dependent variables and Type 1 regressors. When their presence in both sets is
detected by the program, the system is estimated by FIML. It is the user's
responsibility to ensure that identifying restrictions are imposed on the equations,
in this case.
In vector ARMA and GARCH models specified in the Dynamic Equation dialog,
the lags of all the variables are included by default in each equation. For example,
a VAR(2) system of three equations has 6 regressors in each equation. Of course,
some of these regressors can be suppressed if desired, by fixing their coefficients
at 0 in the Values dialogs.
Note that a VAR can be set up in either the Linear Regression dialog or the Dynamic
Equation dialog. In the first case it will be estimated in two steps, by SUR
(equivalently OLS, if unrestricted). In the second case it will be estimated
numerically, by Least Generalized Variance or ML.
15. OUTPUT CONVENTIONS
The outputs from TSM are not always the same as those of other packages.
t-ratios and p-values are not reported in those cases where "zero" is not the
natural null hypothesis for the parameter (variances for example). The Durbin
Watson statistic is not reported by default, since it is often not valid in dynamic
regressions. See the Tests and Diagnostics Options dialog to select it. A valid
LM statistic or M-statistic for residual autocorrelation, or neglected ARCH,
can always be computed if desired, and provides an equivalent test to the DW
in those cases where it is valid. Autocorrelation Q statistics for residuals and
squared residuals are reported by default, as are standard model selection
criteria, although these outputs can be optionally suppressed.
Robust standard errors are reported by default. These will not match the "naive"
(conventional) standard error formulae reported by most packages, and note that
the latter are often based on incorrect assumptions, although they can always be
computed as an option. Heteroscedasticity and autocorrelation consistent (HAC)
12
standard errors are also optionally available. Test p-values and confidence intervals
can also be computed by the parametric bootstrap, based on resampling model
residuals and using the fitted model to simulate data under the null hypothesis.
Asymptotic chi-squared statistics are reported by default for the standard tests of
restrictions and mis-specification, although reporting in 'F-statistic' form is a
selectable option. (Note that in most time series applications, 'F statistics' are
not truly F distributed in finite samples.) Bootstrap p-values can be computed if
desired, for improved test performance in small samples. Another approach related
to the bootstrap is to tabulate test statistics by simulation and use the EDF tabulations
to generate p-values.
0.2 How To ....
For the first-time user who doesn't want to spend too much time with the user's
manual, here are some simple step-by-step instructions to get you started.
1. HOW TO LOAD A DATA SET
*
*
EITHER: click the "Open File" button on the tool bar. In the file dialog,
navigate to the Windows folder containing your data file and click on it.
OR: simply drag the data file icon from the Windows Explorer window
and drop it onto the TSM window.
Several different file formats are supported, but an Excel worksheet is a
popular choice. The series should be stored in columns, starting in column 2,
with the first row of the spreadsheet containing the variable names.
2. HOW TO PLOT DATA SERIES
*
*
*
Click with the mouse on the variable list in any open dialog.
Click the "Chart" button on the toolbar, to display plots of all the highlighted
series on the list.
Clicking the "Chart" button without first clicking a variable list opens the
Graphics / Show Data Graphic dialog.
3. HOW TO RUN A SIMPLE REGRESSION.
*
*
*
*
*
*
*
*
Click on the "regression scatter" button to open the Linear Regression dialog.
In the Select Estimator box choose Ordinary Least Squares (the default).
Choose the dependent variable from the list, and highlight the name by
clicking on it with the mouse. At most one name can be selected at once.
Note that the radio button is highlighted to show you have made a selection
In the "Select Regressors" panel, click on the "Type 1" radio button. Then
select the regressors from the list, as for the dependent variable. Any
number of names can be selected. The radio button is highlighted.
Click the check-box for Intercept, and, if appropriate, for Trend.
To ensure your selection of variables is as you intend, it's a good idea the
click alternately on the highlighted radio buttons. Note how your selections
on the data list are highlighted in turn.
Click the "Go" button in the dialog - or the "Running Man" or "Calculator"
buttons on the tool bar. All have the same action, in this case.
The results appear in the window. To view the Actual-Fitted and Residual
plots, click the "Twin-Graph" button on the tool bar.
13
*
*
To use less than the complete sample for estimation, click the "Select
Sample" button to open the sample-setting dialog. Use the scroll bars to
select the first and last observation.
When you launch an estimation run, open dialogs are closed automatically
to show the results window. Click the "Windows" button on the tool bar
to restore them to their previous locations on the screen.
4. HOW TO GENERATE QUARTERLY DUMMIES
*
*
*
*
Click the "f(x)" button on the tool bar.
Click the Edit button, then scroll down the choice widget (pull-down menu)
until you find "Make Seasonals".
A scroll bar to choose the frequency appears. Select "4", and press Go.
Four dummy variables are added to the data set. Add only three of them
to your regression if you have an intercept!
5. HOW TO TAKE LOGARITHMS OF YOUR DATA
*
*
*
*
*
Click the "f(x)" button on the tool bar.
Click the Transform button, then scroll down the choice widget until you
find "Logarithm".
Highlight all the variables on the list you wish to transform.
Click Go. The transformed variables are added to the data set, identified
with the prefix "Log-" added to the name.
To give a more convenient name, if desired, select Edit and Rename with the
choice widget, and enter the new name in the field provided.
6. HOW TO TEST THE SIGNIFICANCE OF THE REGRESSION
*
*
*
*
The following procedure provides a valid time series implementation of the
"F test of the Regression" reported routinely by many packages. It tests all
exogenous regressors, but automatically excludes the trend, seasonal
dummies, and lagged dependent variables from the test set. Thus, the null
hypothesis can be a valid univariate representation of the dependent
variable.
In the Linear Regression dialog, check "Wald Test of Constraints".
Use the button beside the checkbox to open the Constraints dialog, and check
the box "Test Joint Significance of Regressors".
The test is computed by running the regression, or by choosing Actions /
Compute Test Statistics / Wald Test of Set Restrictions.
7. HOW TO TEST FOR A UNIT ROOT
*
*
*
*
Open the Setup / Compute Summary Statistics dialog.
Check the "Report I(1) Tests" checkbox.
Choose the variable you want to test and press Go.
The Augmented Dickey-Fuller test and Phillips-Perron statistics are among
the results reported. The order of lags in the ADF test is chosen automatically
to optimize the Schwarz model selection criterion over the range up to M =
O(T^1/3). The bandwidth settings for the Phillips-Perron test can be changed
in Options / General...
8. HOW TO ESTIMATE AN ARMA(p,q) MODEL
*
Click the "Space Shuttle" button on the tool bar to open the Dynamic
14
*
*
*
*
*
*
*
*
*
Equation dialog. (If this is not shown, open Options / General, check
"Enable Optimization Estimators", and restart TSM.)
In the Select Estimator box, choose Least Squares.
Select your dependent variable from the list.
Use the scroll bars to select the desired AR and MA orders (p and q).
Select a Type 2 intercept (this is identified even if you have a unit root).
You cannot have both types at once, so deselect the Type 1 intercept
first, if necessary.
Press "Go", or the "Running Man" button.
If your run has been successful, you should see "Strong Convergence"
in the results window.
If you aren't sure what p and q to choose, you can have the program try
each pair in succession up to a chosen maximum. Click Setup / Multiple
ARMA Models... and select the maximum values you want to try.
Click the Running Man with this dialog open, and see the estimates
computed successively in the results window.
You can choose a preferred specification by comparing the Akaike,
Schwarz or Hannan-Quinn selection criteria for each model.
To estimate an ARIMA(p,1,q) model check the "Impose Unit
Root" box.
9. HOW TO FORECAST WITH AN ARMA/ARIMA MODEL
*
*
*
*
*
*
Having selected your model, choose Options / Forecasting..., and use the
scroll bar to select the number of post-sample periods to forecast. Note
that you cannot forecast beyond the end of the data set if your model
contains exogenous variables.
Select the options "Ex-ante Multi-Step" and "Analytic".
Now open the Options / Output and Retrieval dialog, and in the panel
Print in Results Window, check the option "Forecasts & MA Coeffs".
If the model has already been estimated, click the "Calculator" button on
the tool bar. This will evaluate the model and forecasts. Otherwise, click
"Running Man" to run the estimation and forecast calculation in one step.
To see the point forecasts and confidence intervals graphically, select
Graphics / Ex-Ante Forecasts.
The forecasts can also be exported to a spreadsheet file. Click File /
Listings / Save Forecasts.
10. HOW TO ESTIMATE A SIMPLE VAR MODEL
*
*
*
*
*
*
Open the Linear Regression dialog and check the box "System of
Equations". You are now allowed to select two or more dependent
variables.
In the Select Regressors panel, click on the Type 2 radio button. Make the
*same* selections as you made for the dependent variables.
Use the Lags scroll bar to choose the VAR order.
Select an intercept, if desired. Any exogenous variables can be added to
the model as regressors of Type 1.
Press "Go", or the "Running Man" or "Calculator" buttons to estimate the
model.
Note that when endogenous variables are entered as Type 2 Regressors,
the current values are automatically suppressed, making it easy to specify
lagged dependent variables.
15
*
A VAR or VARMA can also be estimated in the Dynamic Equation dialog.
11. HOW TO ESTIMATE A GARCH MODEL
*
*
*
*
*
*
*
*
Open the Dynamic Equations dialog.
Specify the 'mean equation' as appropriate. This could be an ARMA, or
a regression model, for example.
In the Select Estimator panel, choose Gaussian ML.
Click on Conditional Variance Model. The Conditional Variance dialog
box opens.
Select the GAR and GMA orders.
To see the model in the form usually reported (the 'Bollerslev form') open
the Options / ML and Dynamics dialog box and, under "GARCH Settings",
uncheck the first two checkboxes. (Note, the model you fit is identical in
either case. Only the interpretation of the coefficients is affected by these
options.)
Press the Go or Running Man buttons to estimate.
Estimation of GARCH models can sometimes be tricky. Poor starting values
can cause convergence failure. See Help / Hints and Tips for advice on
optimization in case of difficulty.
16
1. User Interface
1.1 The Menus
Clicking on most menu items opens a dialog in which program settings can be
changed. As many dialogs as desired can be open simultaneously.
*
The File menu controls loading and saving of settings, data and results.
*
The Setup menu controls basic operations including choice of data set and
sample size, data editing and transformations, storing and loading models,
special estimation routines, preliminary data analyses, Monte Carlo
experiments, and a test tabulation viewer.
*
The Model menu gives access to dialogs for setting model specifications.
The "Load a Model..." and "Save Current Model" menu items provide a quick
link to the basic Model Manager operations.
*
The Values menu is for setting starting values and selecting options for model
parameters.
*
The Actions menu does things. Some of these menu items open dialogs, but
most perform actions directly.
*
The Graphics menu is to display graphs. An estimation must be run before the
equation graphics options are available.
*
The Options menu is to change program settings.
*
The Help menu gives access to the complete user's manual (also available in
PDF format) and the list of data names and descriptions, if these have been
created. It also contains commands to open the Registration dialog and
"About" window.
Notes:
1.
Close a dialog by clicking the "Close" button ([X]) on the menu bar.
2.
Positions on the screen of closed dialogs are remembered, even between
sessions. This allows the user to create a personalized work layout on the
desktop. Use the Reset Dialog Positions command to centre all dialog
positions.
3.
Submenus and menu items are "greyed out" when the command is currently
unavailable. For example: a data file must be loaded before any action apart
from changing options is possible.
4.
Model options (e.g. Conditional Variances, Regime Switching) can be
switched on and off without altering the settings. To activate a model option
either check the "Active" checkbox in the dialog, or select the option in the
Model / Dynamic Equation dialog. Just setting the required options in the
17
dialog does not activate the option automatically!
5.
Values dialogs will not reflect a change in the model specification until either
the dialog is refreshed or the Values button is pressed in the relevant dialog.
6.
If a dialog gets hidden behind others, bring it to the top by reselecting it from
the menu bar.
1.2 Status Bar and Tool Bar
The status bar at the bottom of the results window shows:
*
the name of the current data set,
*
the currently selected estimator and currently selected sample,
*
the current run ID number.
The symbol "(B)" also appears if bootstrap inference is selected, and the
symbol "(S)" if subsampling inference is selected.
The tool bar buttons provide quick access to the most frequently used actions and
dialogs.
*
"Open Folder" button: shows the File / Data / Open... popup menu by
default.
When the "Load Multiple Data Sets" option is enabled (see Options
/ General), shows the Setup / Data Sets / Switch To... popup menu.
*
"f(x)" button: opens the Setup / Data Transformation and Editing dialog
*
"MM" button: opens the Setup / Model Manager dialog.
*
"Regression line" button: opens the Model / Linear Regression dialog.
*
"Space Shuttle" button (optional): opens the Model / Dynamic Equation
dialog
*
"Running Man" button (optional): normally, launches Actions / Run
Estimation. Also duplicates the function of the "Go" button in an open
dialog.
*
"Calculator" button: launches Actions / Evaluate at Current Values. This
is equivalent to Actions / Run Estimation in the case of linear regression.
*
"Chart" button: Dual action.
o
Displays the plot of the variable(s) selected in the variable list in
any dialog (first click the list).
o
Opens the Graphics / Show Data Graphic dialog if no variable list
has the focus.
*
"Double Chart" button: displays combined chart of actual and fitted values,
and residuals. Only available following an estimation run. Optionally, can
also show the actual-fitted scatter and residual histogram and kernel
density (see Options / Graphics).
18
*
"Dialog 1" button: can be assigned by the user to open any dialog lacking a
dedicated toolbar button. By default, it shows the last dialog opened.
Up to 6 assignable buttons are available, but only the first one is visible by
default. To assign a button, go to the Options / General dialog. See
Section 8.8 for details.
*
"Windows" button: Toggle action.
o
Restores dialogs in previous positions (duplicating Actions / Restore
Dialogs) if dialogs closed,
o
Closes all dialogs (duplicating Actions / Close All Dialogs) if dialogs
open.
*
"Stop" button: only displayed when an iterative calculation is in progress.
Pauses the calculation and opens a choice box, to Abort or Continue.
Notes:
1.
The "Space Shuttle" and "Running Man" buttons can be optionally omitted
from the button bar (deselect "Enable Optimization Estimators" in Options /
General). This option can be used to simplify the interface for classroom
use.
2.
When TSM is running, two "TSM" icons appear on the Windows task bar.
The icon enclosed in a white square represents Ox, running in a minimized
console window. Click it to view the window. The icon without the white
square represents the GUI "front end" running under the Java Runtime
Environment.
Note: if TSM is started by clicking on a settings file in Windows explorer,
the Windows “DOS box” icon appears instead of the first TSM icon.
3.
The "Windows" button remembers which dialogs were open between
sessions. If the "Remember Dialog Positions" checkbox is checked in
Options / General. Pressing it at start-up restores the window configuration
existing at a recent close-down. To avoid an excessive clutter of dialogs
getting re-opened the configuration is reset if the time lag between sessions
exceeds 11 hours.
4.
When lengthy computations such as optimizations, recursive estimations,
grid plots, and Monte Carlo experiments are running, a "Stop" button
appears on the tool bar. Clicking the button opens a choice box, with the
choice of aborting the run or continuing.
Note: there may be some delay before the box opens.
5.
If a panel data set is loaded, the program switches to 'Panel Data' mode
and the "Space Shuttle" and "Running Man" are automatically omitted from
the button bar. Modelling options are selected from the Linear Regression
and Panel Data dialogs in this case.
1.3 The Results Window
The text area is editable. Comments and aide-memoires can be typed in and saved
19
with the output.
*
Text can be highlighted with the mouse, hold down the mouse button and
drag the "I-beam" cursor.
*
Use the right mouse button to open a context menu, with commands to cut
or copy the text to the Windows clipboard.
*
The TSM command File / Save Selected Text allows highlighted text to be
written to a named file.
*
Highlighted text can also be "dragged and dropped" into another application
such as Word or Notepad. Hold down the Control key while dropping
to drop a copy, while leaving the original behind.
The results for an estimation run are printed with a heading showing the version
number of the program, a run ID number and the date and time.
*
The run ID number is incremented each time an estimation is run, and also
each time a stored model is loaded.
*
The ID number is used to identify retrieved series, and also listings, graphics
and settings files optionally generated in the run. This makes it easy to
verify which piece of output goes with which run, at the end of a session.
*
The current ID is stored in the file settings.tsm. It is preserved when settings
are restored to defaults (File / Settings / New). It is reset to 0 only when
settings.tsm is deleted.
*
It can be assigned a new value (zero or otherwise) by going to Options /
General / Special Settings and selecting "Initialize Run ID".
The text size can be changed from the default of 12-point in the Options / General
dialog.
The window can be resized by dragging the corner with the mouse, and also
maximized to fill the screen.
Dialogs are displayed on top of the window. In maximized display mode,
they can conveniently be arranged on the right-hand side of the screen, with the
results printed on the left-hand side.
The command File / Load Text File allows the window to be used as a text
editor. To save text, highlight it and use the File / Save Selected Text command.
*
This feature allows a user's code to be conveniently edited "on the fly",
without needing to start up OxEdit. The command File / Restart closes
and restarts the program in exactly its previous state, including window
contents, allowing the amended code to be compiled.
20
1.4 Dialogs
Dialogs are where most interactions between user and program take place.
They contain objects of the following kinds
Buttons:
Checkboxes:
Radio Buttons:
Choice Widgets:
Scrollbars:
Text fields:
Lists:
to initiate actions, including opening/closing other dialogs.
to turn program options on and off.
to choose from a set of mutually exclusive options.
also known as pull-down menus, to make a choice from a list
of mutually exclusive options.
to input numerical values, usually integers, e.g. sample size.
to input strings of characters from the keyboard. These may
represent names to label the output, or real numerical values.
columns of names, usually of data series, that can be selected
and deselected with the mouse.
Notes:
1.
In model specification dialogs, the choice of radio button may determine the
interpretation of list selections. The correct sequence of actions is:
*
Click the radio button to select the type of variable.
*
Click list items to select/deselect them.
To avoid unintended choices it is a good practice, before launching an
estimation run, to click each radio button in turn, and note which variables
are highlighted in the list for each case.
2.
Choice widgets are similar in function to radio buttons, convenient for
larger numbers of alternatives. The widget shows the current selection in
the window. Click the down-arrow to display the list, which can be
scrolled if necessary, then click the desired selection.
3.
Lists are equipped with vertical scroll bars when there are more items than
can be displayed at one time. Drag the bar to bring them into view.
Horizontal scrolling allows long names to be viewed. On occasion Java can
fail to display the scrollbars correctly. If this happens try closing and
re-opening the dialog, or just drag on the list to scroll it.
4.
In some cases (e.g. selecting the dependent variable) only one list selection
is allowed at a time. In others, multiple selections are allowed. Clicking a
name has a toggle action, select when unselected, deselect when selected.
In some dialogs, double-clicking a list item simultaneously selects the item
and launches the appropriate action on it, e.g. displaying a plot.
5.
There are two ways to quickly select a block of adjacent names on a list.
One way is to select the first name of the block and then select the last
name using the *right* mouse button. This action highlights all the names in
between. Another way is to use 'drag-select'. In other words: click the first
name, then click the last name and drag the mouse briefly with the button
held down, Again, all names between are highlighted.
Deselection of a selected block works in the same way - click the first
highlighted name, then either right-click, or drag, the last highlighted name.
Use the "Clear" button to deselect the whole list.
21
6.
The dialog object most recently clicked on is said to 'have the focus', and is
outlined by a broken rectangle. If the variable list of any open dialog has the
focus, clicking the "Chart" button on the toolbar displays the plot of the
highlighted variable(s).
Note: The current settings in the Graphics / Show Data Graphic... dialog
control what items are plotted.
7.
Options may be "greyed-out" (disabled) if they are not compatible with other
selected options. For example, GARCH and Markov switching options are
not available unless a maximum likelihood estimator is selected. In some
cases, a reminder message is displayed if an illegal selection is attempted.
8.
Make a selection with a horizontal scrollbar by dragging the slider, or by
clicking the arrow buttons at each end, for step-by-step selection. Some
scrollbars (e.g. for numbers of Monte Carlo replications) are incremented
in jumps (10s, 100s) depending on the range of the selection.
1.5 Entering Formulae
Algebraic formulae can be submitted to the program in five contexts.
A.
Data transformation
B.
Nonlinear parameter constraints
C.
Nonlinear equations for estimation or simulation (including equilibrium
relations, nonlinear MA terms and nonlinear ECMs)
D.
Random shock generation for simulations.
E:
Automatic ("on the fly") data transformations.
Formulae are typed into a text box which is opened by the following commands:
Case A:
Setup / Data Transformation and Editing / Formula ...
Setup / Make Data Formula...
Case B:
Model / Constraints / Enter Code (select "Coded Restrictions")
Case C:
Model / Coded Function.
Case D:
Options / Simulation and Resampling / Enter Formula (Select
"Formula")
Case E:
The formula is entered in the variable's description field, preceded
by #FN (case sensitive).
TYPING FORMULAE
The general syntax in cases A, B C is of the form "name = formula",
Case A:
"name" is a new variable name
Case B:
"name" is an existing parameter name.
Case C, "Equation": "name" is optional (must match selected dependent
variable(s) in Dynamic Equation dialog).
Case C, "Residuals": Omit "name" and " = " (formula implicit).
Case D:
Omit name and "=".
Case E:
Omit name and "=". Precede formula by #FN.
A formula can be constructed from the following components depending
on the formula type, as indicated.
ACDE:
Variables, by name or number (see Notes 1, 4) optionally
22
followed by an integer lag (negative) value or lead (positive) value,
enclosed in braces {}.
BCD:
Parameters, by name or number (see Notes 1, 5).
ABCDE:
Real numeric constants, containing digits 0-9, optionally including
a decimal point (.) and optionally preceded by a minus sign (-).
ABCDE:
The operators + (add), - (subtract), * (multiply), / (divide),
^(raise to a power).
ABCDE:
Parentheses (...) enclosing sub-formulae.
ABCDE:
The functions log( ), exp( ), cos( ), sin( ), tan( ), atn( ), abs( ),
sqrt( ), int( ), sgn( ), pos( ), neg( ), flr( ), ips( ), ing( ), izo( ),
and imi(), where the parentheses can contain a variable,
parameter, constant or sub-formula.
ABCDE:
The names Pi, pi, PI and pI are reserved, and are replaced by
the constant 3.14159..., to machine accuracy.
Notes:
1.
The first character of a variable or parameter name MUST be a letter
(from the sets a-z, A-Z).
2.
The following characters can also appear in variable or parameter names:
!#$%&',0123456789:;<>?@\_~|
3.
Names are case-sensitive! E.g. 'Alpha', 'ALPHA' and 'alpha' are all
treated as different names.
4.
An alternative to typing a variable name in full is to type x[i] or X[i] where
"i" denotes the number of the variable in the data list. When the text field is
opened, variable numbers are pre-pended to names in the appropriate
data list , i.e.:
*
In case A, Setup / Data Transformation and Editing
*
In case C, Model / Dynamic Equation.
5.
An alternative to typing a parameter name in full is to type a[i] or p[i] or
A[i] or P[i] (all forms are equivalent) where "i" is the parameter number.
Parameter numbers are shown in the Values / Equation dialog(s).
6.
The characters +-*/^.()[]{} must NOT appear in names of variables or
parameters. Any other characters, in particular spaces, are ignored. Use
spaces optionally to improve readability.
WARNING: Variable names generated automatically in Setup
/ Data Transformation and Editing may contain illegal
characters!!
Rename such variables before including in a formula.
7.
The * sign to denote multiplication is mandatory. Omitting it will cause a
23
syntax error.
8.
Numeric constants can contain the symbols .0123456789
The symbol "." (decimal point) may appear ONLY as part of a numeric
constant. An isolated "." is parsed as the number 0.
9.
Constants are nonnegative. A leading "-" (minus) in any formula is parsed
as a unary operator, and changes the sign of the operand.
10.
Definitions of special functions:
atn(x) = arctan(x).
sgn(x) = -1 if x < 0, 1 otherwise.
pos(x) = x if x > 0, 0 otherwise.
neg(x) = x if x < 0, 0 otherwise.
int(x) = integer nearest to x.
flr(x) = largest integer not exceeding x.
Indicators:
ips(x) = 1 if x > 0, 0 otherwise.
ing(x) = 1 if x < 0, 0 otherwise.
izo(x) = 1 if x = 0, 0 otherwise.
imi(x) = 1 if x = NaN (missing observation), 0 otherwise.
These functions are not differentiable, so may not be used in parameter
constraints. This results in a parsing error.
Also note:
pos(x - y) + y = max(x, y)
neg(x - y) + y = min(x, y)
x - y*flr(x/y) = x mod y (x,y integers)
1 - ips(y - x) = 1 if y <= x, 0 otherwise
etc, etc. Other uses include creating period dummies. If t is an integer,
dummy = neg(pos(Trend - t) - 1) + 1
= 0 up to date t, 1 from date t onwards.
11.
Reminder: the following uses are mandatory!
*
Parentheses ( ) for function arguments and sub-formulae;
*
Square brackets [ ] for parameter/variable numbers;
*
Braces { } for lags and leads.
12.
If the formula cannot be parsed (e.g. non-matching parentheses, missing
operators) an error message is printed and the calculations are terminated.
If an operation is illegal (e.g. square root of negative number) the output
of the formula will be NaN.
RESERVED NAMES
13.
The reserved names U#, u#, and N#, n# (upper and lower case equivalent)
are treated differently depending on the function call.
Cases ABE, C in an estimation run:
Assigned the value 0.
Case C in a simulation run:
U# and u# are replaced by a uniform[0,1] random drawing, and
N# and n# are replaced by a standard normal random drawing,
playing the role of a randomly selected parameter. This feature
24
allows the generation of randomized models for (e.g.) test power
evaluation.
Case D: U# and u# are replaced by a sample-dimension vector of
uniform[0,1] random drawings, and N# and n# are replaced a
sample-dimension vector of standard normal random drawings.
If the symbols appear more than once in a formula, a different drawing
(vector of drawings) replaces each.
14.
(Cases AC)
The variable names E#{-j}, e#{-j}, where j represents a positive integer,
are reserved for use in recursive functions. They are replaced by the
function value itself lagged j periods. E# without a lag is replaced by 0.
In systems of equations, the names E#1, E#2, ..., and E#1{-j}, E#2{-j},
..., denote the values for each equation, current and lagged respectively.
Current values from lower-numbered equations can appear in highernumbered equations, otherwise are replaced by 0.
15.
(Case C)
The variable names Z# and z# are reserved for use in nonlinear ECMs,
and are replaced by the values of the equilibrium relation. In models with
two or more equilibrium relations, use Z#1, Z#2, ..., to denote the values.
16.
(Case C)
The variable names W#, w#, and also W#{-j}, w#{-j} and where j
represents a positive integer, are reserved for use in simulation models.
These represent the random shock used to generate the series, current
and lagged j periods, respectively. In systems of equations, the names
W#1, W#2, ..., etc., denote the shock values for each equation.
NOTE: Attempting to estimate a model with this option generates an
error. Equations in which the current shock enters nonlinearly cannot
be inverted automatically. To estimate a model of this type, create the
specification in a separate model.
17.
(Case C)
The variable names X#[i] and x#[i], where i >= 0 denotes the position
of a variable in the data set, as in 4 above, cause the indicated variable
to be over-written by a column of standard normal random numbers
before a simulation is run. Leads and lags are accessed in the usual way,
by entering X#[i]{-1}, etc. When estimating a model with this option
selected, the "#" is ignored and X#[i] is equivalent to X[i].
18.
(Case E)
The variable names S# and s# denote the variable being transformed.
1.6 File Drag-and-Drop
Data and settings files can be loaded by dragging the icon(s) from Windows Explorer
and dropping over the program window.
*
The action taken depends on the file extension.
*
See 2.2 File / Data for a list of the supported data file types.
*
Multiple file drops are supported. Cases where only single file drops allowed
25
*
are indicated by (S).
Special actions are performed on files with the indicated name prefixes.
File Type
---------settings file (.tsm)
model file (.tsd)
data file
text file (.txt, .ox, .h)
data file, "EDF_"…
data file, "DNS_"…
.tsd file, "Batch_Run"…
Equivalent Menu Command
---------------------------------File / Settings / Open... (S)
File / Settings / Import Model...
File / Data / Open...
File / Load Text File
File / Data / Tabulations / Load EDF Table. (S)
File / Data / Tabulations / Load Density Plot. (S)
File / Data / Tabulations / MC Batch Results. (S)
26
2. File
2.0 File: General Information
This menu gives access to submenus for:
Settings
>>
Save and load ".tsm" files.
Data
>>
Save and load data files, including empirical
distributions for test statistics.
Results
>>
Control the saving to a file of output from the results
window.
Listings
>>
Save items of output from estimation or simulation runs
to spreadsheet files.
Graphics
>>
Save a copy of the most recently displayed graphic.
Load Text File
Allows the results window to be used as a text editor. The
contents of the chosen file will be appended to the existing
window contents.
Save Selected Text
Allows any part of the text in the results window to be saved to
a file. Give this command after highlighting the desired text by
dragging with the mouse. The options presented are to append
the text to the current results file, and to write to (overwrite) a
new (existing) named file.
Restart
These options close the program and automatically restart it
with all run settings intact, including results window contents.
These are convenient shortcuts for loading user's code.
In some situations a manual restart is necessary, see Notes.
>>
Restart/Load User Code
A choice box gives the options of loading the currently
specified user Ox code, and selecting a different code
file in the file dialog.
Restart/Load Text Input
A choice box gives the option of selecting a text file containing
a set of TSM text commands, for loading as program settings
and/or model specifications.
Restart/Load Text Defaults
Loads default settings which (if different from the programmed
defaults) will be set with the File / Settings / Clear All
command, and also if the settings file is renewed.
Quit
Closes the program. The prompts to save specification and
data before closing can be optionally switched off; go to
Options / General.
Notes:
1
Selected text can be cut, copied or deleted. After highlighting, click the right
27
mouse button and select from the context menu.
2.
The contents of the Windows clipboard can be pasted into the results window
at the cursor position. Right-click with the mouse, and select "Paste".
MRU LISTS
3.
Commands for loading, saving and exporting settings and data files open a
popup menu listing the most recently used (MRU) files. The leading item,
'File Dialog...', opens the operating system's file dialog for selecting other
files.
4.
If a list is empty, the popup menu is skipped and the file dialog opens
directly.
5.
The maximum number of files on the MRU lists is an installation option see Appendix B. The default setting is 20.
6.
MRU lists are stored in the settings file. When settings are loaded the
current lists are appended to the new ones, as space permits.
FILE DIALOG
7.
The file dialog is sensitive to the type of file being loaded/saved, and presents
only files of the appropriate type for selection, specified by extension. (See
Section 11: Directories and Files for details.) Use the "Files of Type:" choice
widget to present different categories of file types, where appropriate.
RESTART
8.
The restart options work automatically only if the program is launched from
the Windows Start Menu. If started in Windows Explorer (by doubleclicking on a .tsm file) the restart must be performed manually after the
program closes, by double-clicking "settings.tsm". However, the main feature
of the restart mode, the preservation of the results window contents, is
operative in this case.
9.
The Restart/Load User Code command causes the file "usercode.ox" to be
created if necessary, then edited to contain the line
#include "[chosen file]".
The chosen file must have extension '.ox'! If necessary, the executable Ox
file tsmod_run.ox is also edited to include and #define USER_CODE '
' #include "usercode.ox" ' compiler directives.
Notes:
*
Only one code file at a time can be compiled. Any other '#include...'
statements are deleted from usercode.ox. Other lines are
commented out.
*
The currently stored usercode file name is used by default. Open
the file dialog at the prompt to select a different one.
*
To remove the currently loaded code file from memory, open the
file dialog at the prompt and press "Cancel".
10.
The Restart/Load Text Input command causes tsmod_run.ox to be edited
to include the directive '#define TEXT_INPUT ' and the statement
28
' Text_Input(){ #include "[chosen file]" } ', which include the contents
of the chosen text file as lines in the Text_Input function. After the restart,
these lines are deleted to restore tsmod_run.ox to its previous state.
10.
The Restart/Load Text Input command causes tsmod_run.ox to be edited
to include the directive '#define TEXT_INPUT ' and the statement
' Text_Input(){ #include "[chosen file]" } ', which include the contents
of the chosen text file as lines in the Text_Input function. After the restart,
these lines are deleted to restore tsmod_run.ox to its previous state.
11
Normally, the text file will contain either a complete specification for the
(non-default) program settings, or a complete (non-default) model
specification. In these cases it is usually important to set the defaults before
importing the new settings. In the first case, do this by setting the first line
of the file to
Set_Defaults();
In the second case, set the first line of the file to
Set_ModDefaults();
Failure to include one of these lines may lead to unpredictable results.
12.
If the new settings include parameter values, then the last line of the file
must be set to
Load_TextValues();
This function converts the new values to the internal program format. If it
omitted, the new values will be ignored. Note, it is not possible to read
in a subset of new parameter values and retain others. Running this function
resets all the parameters.
13.
The Restart / Load Text Defaults option edits tsmod_run.ox with permanent
effect. To restore the standard default settings, edit the file and comment
out the '#define TEXT_DEFAULTS' line. The defaults file can also be
modified in a text editor. See the programming manual for information on
text commands.
14.
If the Restart command is given after editing the user's code, resulting in a
compilation error, the program will fail to restart. In this event, check the
console window for error messages. TSM can always be restarted using
the default shortcut if required. This shortcut uses the unchanged copy of
tsmod_run.ox in [TSM-HOME].
15.
Use 'Simple Restart' for option changes that require a restart, such as
hiding/showing advanced estimation features.
2.1 File / Settings
Settings files (extension ".tsm") save the current state of the program, including
optional program settings, model specifications, and parameter values. If the option
to save the specifications was selected when it was saved, loading a settings file
recreates the exact state of the program at that time, including operational settings,
model specifications and starting values. Otherwise, it restores the operational
29
settings only.
The file settings.tsm in the working directory is automatically loaded at start-up, if it
exists. It is saved (with the model specifications and starting values) before each
estimation call, and also at shutdown. The current state can be saved at any time in a
named settings file, and reloaded subsequently.
The available commands are
Open…
Loads settings from a selected file. Only files with extension
".tsm" can be opened.
Import Model...
Adds a model specification stored in a ".tsd" file to the
current settings.
Save
Saves settings to the default file, "settings.tsm".
Save As...
Saves settings to a named settings file. The extension ".tsm" is
added to the file name if not supplied.
Export...
Exports settings, listings and data to a .tsm file.
Settings as Text
>>
Display/Save Settings...
Writes all the non-default settings as text, in TSM script
format, either to the results window or to a file.
Save Current Model...
Writes the non-default specifications for the currently
loaded model to a file
Save System Defaults...
Writes the current system settings as text.
Clear
Replace all settings with defaults (see Options / General
Information and Defaults for a list.)
Notes:
1.
Settings are saved automatically to the default file "settings.tsm" before any
estimation run and at closedown. Therefore, there is normally no need to save
them manually, except to a different named file to store them for subsequent
reloading.
2.
In the Windows installation, TSM can be started by double-clicking on
a settings file. This loads the file in question, as if loaded by the "Open..."
command. Note that settings are saved to the default "settings.tsm" as usual.
Use "Save As..." to update a named file.
IMPORTING MODELS
3.
The "Import Model..." command can be used to access model specifications
stored in .tsd files (which can include data sets) created with a different
settings file, or a different installation. This option (which replaces a
superseded import command that operated on .tsm files) only works for
.tsd files created with TSM 4.27 and later releases.
30
4.
If a model is imported which has the same name as an existing model,
its name is modified by adding a % character.
EXPORTING SETTINGS
5.
6.
The "Export..." option allows model specifications to be distributed to other
users. This option has the following features:
*
All relevant information is saved in the .tsm file, including the current
data set(s), model listings (usually saved in separate .tsd files), and
supplied Ox code.
*
All local path information, including MRU lists, is omitted from the
file.
*
When the file is loaded, the stored data and listings files are
automatically saved in the local "Start-in" directory. In this way,
the local installation can exactly reproduce the set-up existing
on the machine where the 'export' file was created.
To be exported using "Export...", supplied Ox code must be contained
in one of the following locations:
1)
The standard file "usercode.ox" located in the Start-in directory;
2)
7.
The file named in a "#include" compiler directive in "usercode.ox".
In this case,
*
any executable code in "usercode.ox" itself is ignored.
*
only the first "#include" directive in "usercode.ox" is
recognized. Any additional inclusions are ignored.
Any text in the results window which is highlighted when the File / Export...
command is given is stored in the settings file, and written back to the
results window at start-up. This trick allows instructions and notes about
the contents of the exported file to be easily conveyed to recipients of the
file.
SETTINGS AS TEXT
8.
The "Display/Save Settings" command opens a choice box, with the options
of printing the text in the results window, and opening the file dialog for
saving the text. In the latter case, a ".txt" file extension is recommended.
See the programming manual for details of the scripting language.
9.
The "Save Current Model" command saves just the loaded model settings to
a file. To view these settings in TSM, store the model in Model Manager with
the "Automatic Descriptions" option checked, then click the "Model
Description" button. The main function of this command is to allow the
settings to be imported into another instance of TSM using "File / Restart /
Load Text Input".
10.
The "Save System Defaults" command saves a file for loading at start-up.
This options allows the user to control the state of the program set by the
File / Settings / Clear All command, or renewing the settings file. Use the
31
File / Restart command to set up the system to read the designated file.
2.2 File / Data
Data can be read and written in one of eight formats. The format is specified by the
file extension.
".xls", ".xlsx"
Excel 2003 and 2007 worksheets. The first row of the sheet
must contain variable names.
".csv"
Comma delimited text file. Format as for .xls.
".in7"
GiveWin file. See OxMetrics documentation for details.
".dht"
GAUSS data file.
".dta"
STATA (Versions 4-6) data file.
".dat"
OxMetrics "data with load information" file. See the
documentation for details.
".mat"
ASCII file containing a matrix, with variables in columns
and observations in rows. The first line of the file must contain
two integers, number of rows followed by number of columns.
In this case the variable names assigned are "Var1", "Var2",
etc. These can be changed in the Data Transformation and
Editing dialog.
Open…
Opens the operating system's file dialog, for opening. Any data
currently in memory are over-written.
Merge…
Merges new file with data already loaded. After selecting the
file, a dialog is presented to enter the 'row offset'; that is, the relative
position in the current file of the first observation of the new file. The
offset is:
>
zero if start dates match,
>
positive if start date of new series is later, or
>
negative if start date of new series is earlier.
Close the dialog either by pressing "Return" or clicking the Close
symbol on the menu bar.
Save
Saves data under the name specified in the last Open or Save As
command.
Save As…
Opens the operating system's file dialog, for saving. The type of file
saved is determined either by the extension or, if no extension is added,
by the current selection in Options / Output and Retrieval Options.
Edit Spreadsheet...
This option opens a "raw" data file for editing, effectively duplicating
32
the role of Excel or similar software.
Notes:
1.
Data files may be loaded by the program automatically, as when a settings
file or a stored model is loaded. If the file in question is not found on the
stored path, other paths known to the program are searched. Messages
are printed to show that this has occurred, or if the file is not found anywhere.
Since the file found might not be the one intended, it is important to check the
program messages.
2.
If data are saved in .MAT format, the variable names are listed in the results
window.
3.
When loading a data set a prompt appears by default, giving the option to
retain or clear the current model specifications. In most cases, these won't be
appropriate to the new data. To make clearing automatic and so bypass this
prompt on future occasions, without disabling the other prompts, choose the
option "Always". To reinstate this prompt, deselect and then reselect the
option "Enable Saving/Clearing Prompts" in Options / General.
DATA DESCRIPTIONS
4.
In addition to names for the series, data files can optionally store text
containing a description of the variable. The description field can be used,
among other things, to contain formulae specifying transformations of
variables to be performed "on the fly" as part of a model specification.
A user-specified, reserved character, @ by default, is used to separate
a variable name from the description field. All characters following the @
form the description. Descriptions for the current data file can be viewed
by the command Help / Data Descriptions, and created and edited in
Setup / Data Transformations and Editing / Edit; see 'Edit Description'.
If desired, the separator character can be changed during installation by
editing the file tsmgui4.oxh and setting the function Get_NameCharacter().
5.
Ox allows a maximum of 64 characters to appear in the name field (the first
row of the spreadsheet), but descriptions can nonetheless be of arbitrary
length. If the name and description together exceed 64 characters, the
additional characters are stored numerically at the bottom of the
corresponding spreadsheet column (a Double value occupies 8 bytes, and
so can represent up to 8 text characters.) The description zone is separated
from the data proper by two rows containing, respectively the constants
"DBL_MAX" and "DBL_MIN" (the largest and smallest storable numbers).
These additional rows can be inspected by loading the file into a program
such as Microsoft Excel.
MISSING OBSERVATIONS
6.
The input file may have missing observations (e.g. blank cells in an Excel file)
and these are replaced in the data matrix by NaN (= Not a Number). If the
variable in question is included in a model, the sample period is automatically
truncated, as necessary, to exclude NaN observations.
33
PERIODIC OBSERVATIONS AND DATES
7.
If provided, date information (years, quarters, months etc.) is used to label
graphs and printouts, and is presented in the Setup / Set Sample dialog for
selecting the sample. Ox dating information is used by default. This is the
first column of any spreadsheet file saved by TSM, and has the format
"Year-Period". This format is suitable when the data have a regular
periodicity, but if other dating schemes are used thus column is ignored, and
can be deleted from the spreadsheet if desired.
For data sets other than panel data, there are three ways in which the user
can create dates.
*
Year-Period: Enter information on the start date and the periodicity and
let TSM generate the dates, which are saved in the default Ox format.
This is the best scheme for annual, quarterly and monthly data, where
the periodicity is fixed.
*
Calendar Dates: Create a literal date series in the data file using the
"yyyy-mm-dd" date format. This is the best scheme for daily data,
where the periodicity is irregular due to week-ends and holidays.
*
Date Labels: These are arbitrary numerical values, which need not be
increasing, or regular, stored as a special series in the data file. These
are suitable for irregularly spaced data and historic long period data
series.
Note: If a file contains more than one type of date information, calendar
dates take precedence over date labels, and date labels take precedence
over Ox-format year-period dates.
PERIODIC DATES
8.
These use the Ox dating format, and is the easiest form of dating to set up.
The date information can be added in TSM using the "Set Dates" command
under Setup / Data Transformation and Editing / Edit. A column is created
with the reserved name !STARTDATE!, and having entries in the first three
row positions, as follows:
1.
The year of the first observation
2.
The period (quarter/month/week/weekday/day) of the first
observation
3.
The frequency: one of
2 (half-years)
4 (quarters)
12 (months)
52 (weeks)
260 (weekdays)
365 (days).
The rest of the column can contain anything, or be blank.
This item is removed after being read, so it will not appear in the variable list.
If the data file is then saved in TSM, it will contain the date information in Ox
format - the first column of the file will contain the dates in the format
"year - period". This column will be used to create date information next time
34
the file is loaded.
9.
If files are merged, the date information of the first-loaded file is used unless
the merged file contains a !STARTDATE! column, in which case this
information is used to date the combined observations. Ox date information in
the merged file is ignored.
10.
The periods must have equal length (e.g. no missing holidays, or leap years,
in daily data). Ignoring these irregularities may be permissible for labelling
graphs, for example.
CALENDAR DATES
11.
To set individual daily dates, load the data file using the command File / Data /
Edit Spreadsheet... Create a new variable with the name "Date" (for example,
use the "Make Zeros" command) and move it to the first position in the file
using the Edit command "Move Up List". Now enter the dates in the format
yyyy-mm-dd (the "Copy" button is useful to propagate the template from
cell to cell). Optionally, times of day can also be entered using the 24-hour
format yyyy-mm-ddThh:mm.
12.
Dating information is used automatically if it is present. To over-ride this
behaviour and set periodic dates in the default manner, use the "Set Dates"
command in Setup / Date Transformation and Editing. In this case, the
existing date information is deleted. If dated files are merged in TSM, the
dating information in both files is ignored.
DATE LABELS
13.
Create a variable in the data file with the reserved name !DATELABELS!.
the elements of this column are used to label the observations. They must be
numeric, but are otherwise arbitrary. For example, in the case of irregularly
spaced data, including just the year, repeated as required, may provide
sufficient information to label a time plot. The labels could also be in
descending order to denote (e.g.) "Years ago".
14.
The label series can be created in TSM using the command "Set Date
Labels" in Setup / Data Transformation and Editing (Edit). The series
is not visible on the variable list, but appears in the dates column when
series are listed, and is saved to a spreadsheet file with the data
15.
If files with date labels are merged in TSM, the dating information in the files
is merged. Labels from the merged file replace existing labels when both exist.
Otherwise, missing labels are replaced by zeros.
PANEL DATA
16.
To load a panel sample, the data file must be formatted according to the
following specifications. The data for each variable must be input as a single
column. The observations on 'individuals' should appear in row blocks, with
the dated observations in date order, within each block.
17.
Panels can be unbalanced, with different start and finish dates for each block.
A date must take the form of either a year, or a period, or a year + period
35
(quarter, month etc.) Dated daily data are not supported.
18.
Panels can also be irregular, with missing periods as well as different startfinish dates. However, irregular panels must have a seasonal frequency of
one (years, or periods). The year + period format is not supported.
19.
The file must contain the following guide columns. They can appear anywhere
in the file.
*
A column with the name !PANEL! (or equivalently !INDIVIDUAL!)
in the first row. This contains the individual identifiers. The same
number or text string (see para 27 below) should appears in all the
rows of an individual block. Numbers need not be consecutive.
(Block boundaries are detected by these entries changing.)
*
A dates column headed with the name !YEAR! or !PERIOD!.
This will typically contain the year of each observation, hence the
sequence is repeated within the individual blocks.
Also, optionally:
*
If a !YEAR! column exists with repeated entries, a column headed
!PERIOD! will contain the quarter/month counts within each year.
*
A column headed !GROUP! can be used to label groups of
individuals, such that all individuals in a group get the same
identifier. Any numbers can be used as identifiers, but the number
0 is always used to flag that the individuals in question are to be
omitted from the analysis.
The guide column names can be written in upper or lower case.
20.
When both !YEAR! and !PERIOD! columns appear in the file, dates are
counted in years and periods, so the !YEAR! column should contain
repeated entries. For example, suppose a panel contained observations
for the five quarters 2001Q2 to 2002Q2 inclusive. The first few rows
of the file should then look like this:
!PANEL!
!YEAR!
!PERIOD!
...(data)
1
2001
2
...
1
2001
3
1
2001
4
1
2002
1
1
2002
2
2
2001
2
2
2001
3
2
2001
4
2
2002
1
2
2002
2
3
2001
2
...
...
...
21.
NOTE: the dating system for panel data is distinct from the usual case,
because Ox cannot maintain panel dates automatically. Saved panel data
sets contain an Ox 'dates' column, but this is ignored by TSM when the
file has the format specified above.
22.
Individuals in a panel may be identified by names instead of numbers.
36
However, because of the limitations of the Ox data file format the
names cannot be stored in the same file as the data itself. Instead, type
the names in order into a text file, separated by spaces or carriage
returns. Save this file to the same location as the data file, and with the
same name as the data file but with extension ".txt". These names are
used in the estimation output to label individual dummies, and also as
row labels in the data spreadsheet.
SPREADSHEET EDITING
23.
Use this option to edit a "raw" spreadsheet or data file. TSM functions
in this mode as a simple alternative to Excel or equivalent spreadsheet
program. This mode is chiefly useful for setting up series of calendar dates,
date labels and indicators, and also for preparing files in panel data format.
24.
When a data file is loaded by this command, the data editing dialog
opens automatically, and all other program functions, except data
graphics, are disabled. Guide series that are normally concealed from
the user - having special names enclosed in !! pairs - are visible, and
can be created and changed as required. When the dialog is closed,
the file is processed in the usual way, and TSM then functions as normal.
25.
In files formatted for panel data, a column headed either !PANEL! or
!INDIVIDUAL! (upper or lower case) contains indicators of the
individuals in the data set. Entries in this column can be either numbers
(positive integers) or text (names not exceeding eight characters in
length). These entries are stored as equivalent double-precision values
in the spreadsheet and converted to text when the file is processed.
Simply type the names into the cells of a column so headed in the
List/Edit table, or use the "Edit Observation" field as usual. Then use
the "Copy" button to fill the required number of rows with the same
entry.
Note:
*
Change in the contents of these rows signals the next individual
in the sample, so the same text (or number) must appear in
each individual block.
*
Non-numeric text can only be entered in a column headed as
above.
*
In programs such as Excel, the default numerical formatting may
show the text fields as zeros! They can only be viewed correctly
in TSM.
26.
A column headed !GROUP! (upper or lower case) contains group
identifiers. These are constructed in the same way as the !PANEL!
identifiers (see 27), but they only need to appear in the first row of each
individual block. The contents of the remaining rows of each block are
optional.
27
If the !GROUP! column is present, any individual block containing 0 as
its first element is omitted from the analysis. This allows individuals to
be included in/excluded from the data set with minimum difficulty. To
disable the column without deleting it, simply rename it. It then appears
37
in the data set as a "variable" when the data are reloaded.
TROUBLESHOOTING
28.
Although Ox should read spreadsheet files such as the Excel .xls format
and .xlsx files, it is occasionally found that such files contain incompatible
features. The message "Data input failed" appears. In this event, use
Excel to save the file in comma delimited (.csv) format. These files are
always readable and contain all the information relevant to TSM
functionality. If TSM is then used to save the data in .xls or .xlsx format,
the file will be readable by both TSM and Excel.
2.3 File / Results
Results and information appear in the program's text window.
The output can be saved to disk files in two ways.
1.
Select part or all of the window's contents, using the mouse, and append these
lines to a designated file.
2.
Have all the output saved automatically to a file, in the background.
Both methods can be used at the same time, if desired.
* Enable Background Saving
Switches on Background Save mode
* Disable Background Saving
Switches off Background Save mode.
* New Results File…
Opens the file selection dialog, showing
the current results file. Choice can be an
existing text file or a new one.
Notes:
1.
Results are always appended to the current results file. To start a new file,
choose a new name, or delete the existing file first.
2.
The default results file is "results.txt", in the working ('Start-in') directory.
This will be created automatically if it does not exist. There is no default name
for selections. You are prompted for a file name if one is not currently
specified. If background saving is enabled, the New Results File command
designates a new file for background saving. If background saving is disabled,
the chosen file will be used for selected text.
3.
If the folder specified for a new results file is different from the working
directory, the results folder is changed accordingly. Listings files and graphics
will be saved thereafter to the same location. However, the settings file must
always reside in the 'Start-in' directory, so it can be found at launch.
4.
To guard against attempting to append text to an existing binary file, results
files must have extension ".txt". This is appended to the chosen name if it is
not present.
5.
Yet another way to save results is to use the Windows clipboard. Just highlight
the desired text in the results window, Copy (right-click for the context menu),
38
and Paste into your favourite text editor.
6.
The 'Locate Results Folder...' command opens a text field containing the
current path to the results folder. This can be edited to change the folder.
Press the "Browse" button to navigate the directory tree and select a folder,
else type the path directly in the text field.
Notes:
*
Selecting a new results file automatically sets the results folder to the
one containing the file.
*
Graphics are always saved in the current results folder.
*
The 'Start-in' directory is used as the results folder by default, but note
that the current path is saved between sessions in "settings.tsm".
2.4 File / Listings
"Listings" refer to outputs generated by the program in tabular or graphical
form. The commands
*
Open Listings File...
*
Save Listings File...
allow listings to be saved and reloaded in a format that can be displayed and/or
further processed by the program. These files have extension ".tsd".
Listings can also be exported in spreadsheet format, for processing by other
software. The command "Export Spreadsheet" gives access to a submenu
containing the following items:
*
Series:
actuals and fitted values, residuals, conditional
variances, regime probabilities.
*
Correlograms:
also Q Statistics for the residuals and squared
residuals corresponding to each lag.
*
MA coefficients:
equivalently, impulse and/or step impulse
responses.
*
Forecasts:
including standard errors and/or confidence
bounds where available.
*
Recursive Estimates: coefficients and standard errors, summary
statistics and test statistics.
*
Recursive forecasts:
*
Criterion plots:
*
Monte Carlo replications (or optionally, relative frequencies).
Notes:
LISTING FILES
1.
".tsd" files are created automatically when a model is stored with Model /
Save Current Model..., or with the Model Manager, and receive the name
assigned to the model. Such files are likewise loaded by the command
Model / Load a Model.... Files created in this way can also be read
using the Open Listings File... command, but in this case there is no change
to model specifications. Saved files can be named in any way desired.
These commands are intended to be useful mainly for storing and
retrieving the results of Monte Carlo experiments.
2.
The command File / Settings / Import / Import Model... also reads ".tsd"
39
files, but in this case model specifications as well as listings are loaded, with
the imported model receiving the name of the file containing it. Use the
command Open Listings File... to load the listings, but without creating a
new model. The "Save Listings File..." command does nonetheless include
the current model specifications in the file. Reading the file with the "Import
Model" command would allow these to be retrieved, if desired.
3.
A ".tsd" file contains all the listings currently held in the program at the
moment it is saved. When the file is loaded, all such items get replaced
in memory. Be sure to save anything you want to keep before loading
a file.
4.
Files with the generic names "Batch_Run??_Inst??.tsd are created when
parallel processing is used to run Monte Carlo experiments. These files
have a special format, and can only be read using the command File /
Data / Tabulations / MC Batch Results... An error message is printed
if an attempt is made to open these files with "Open Listing File".
SPREADSHEETS
5.
Spreadsheet files are saved by default to the currently selected results
folder, under a descriptive name appended with the run ID number,
or optionally through the file dialog.
6.
Available file formats are the same as for data, as selected in Options /
Output and Retrieval. When saving in ".MAT" format, the columns
headings are listed in the results window.
7.
There is an option to save all listings automatically following a run, see
Options \ Output and Retrieval.
8.
By default, the output to the 'Forecasts' spreadsheet contains a
selection of quantiles of the forecast distributions, either from the
bootstrap distribution in Monte Carlo forecasting case, or otherwise
Gaussian. To simplify this output to contain only the point forecasts
(means or medians in the Monte Carlo forecasting case) go to
Options / General / Special Settings, and select "Export Point
Forecasts Only" from the pull-down menu. Double-click the text
field to toggle between settings "True" and "False".
9.
In the 'Recursive Forecasts' spreadsheet, the rows of the table
match the rows of the 'Recursive Estimates' table. The entries in the
first column correspond to the dates from which the forecasts are
projected forward. The j-step-ahead forecasts, for j = 1,2,...,
then appear in successive columns.
This arrangement is in contrast to that of the 'Forecasts' spreadsheet
in which the row count corresponds to the number of steps ahead.
Here, the first column shows the dates of the observations being
forecast.
40
2.5 File / Tabulations
These commands handle special spreadsheet files, formatted to be read as tables for
plotting or critical value calculations.
Load EDF Table...
Loads a previously prepared spreadsheet file containing an
empirical distribution function. This can be displayed in
Setup / Look Up Probability and Setup / Look Up Critical
Value, and used by the program to generate test p-values.
Files with the correct format are generated by the Monte Carlo
module, see Setup / Monte Carlo Experiment.
Merge EDF Table... Combines a selected file with the resident EDF table. When
combining tabulations for different sample sizes, the names and
specifications for the two tests must be identical.
Save EDF Table...
Converts an EDF table held in memory back to a file, reversing
the "Load..." command. Optionally a new name can be entered
using the file dialog, the stored file name is used by default.
Clear EDF Table...
Removes table from memory. The table is saved with model
listings, ('.tsd' files) so use this command before storing a
model to avoid bulky files .
Load Density Plot... Loads a previously saved spreadsheet file containing data for
generating density plots in the dialog Graphics / Stored MC
Distributions. The file contents are merged with any existing
plot data. If a loaded plot has an existing name, the name is
augmented with "(1)".
MC Batch Results... This command duplicates the action of the "Results" button in
the Setup / Monte Carlo Experiment dialog.
Notes:
1.
The files read by these commands must have a spreadsheet format and
extension, but also require special formatting to be read successfully. TSM
optionally creates these files in the course of running simulation experiments.
Alternatively, given suitable data the files might be constructed manually in
a spreadsheet program. The format specifications are given in Appendix G
of the TSM documentation.
2.
EDF tables are stored in the listings (".tsd") file created for a model, and
are loaded along with the model if this file is available. If listings file is
unavailable when a model specifying EDF critical values is loaded, TSM
looks for the specified spreadsheet file. This might be the case if the
estimation job is being run as an external process, in a different location,
for example.
3.
An exported settings (".tsm") file bundles all material relevant to each
stored model, including data sets and EDF tables. When such a file is
loaded, both the data and EDF spreadsheet files are created
41
automatically in the working directory.
2.6 File / Graphics
Save last Graphic >
Saves the most recently displayed graphic to a file.
Optionally, one can either open the file dialog to enter
a name for the graphics file, or accept the default file
name.
Import Graphics Settings... Open the file dialog to select for import a previously
exported store of the settings for the Options / Graphics
dialog
Export Graphics Settings... Open the file dialog to name a file to receive the current
settings in the Options / Graphics dialog. These can be
subsequently re-imported with the Import Graphics
Settings... command.
Notes:
1.
The default file type for saving is set in Options / Output and Retrieval. The
type can also be specified interactively in the file dialog, by the choice of file
extension. The options are '.png', '.gif' (bitmap formats) and '.eps', '.fig', '.tex'
(vector graphics formats).
2.
Font specifications, and bitmap dimensions for '.png' and '.gif' files, are
selected in Options / Graphics.
3.
There is an option to save all graphics automatically as they are displayed;
see Options / Graphics.
4.
Graphics settings files receive the extension '.tsd', and the blue 'TSM
Document' icon, as for model data and batch output files. However, they
can only be read with the Import command in this menu. Attempting to
read them through the File / Import Model... command produces an
error message.
2.7 File / Folders
Use these commands to show and/or change the storage locations of different
types of files used by TSM. A command opens a text field containing the current
path to the folder. To change the path, you can
o
edit the field directly,
o
press the "Browse" button to navigate the directory tree and select or create
a folder,
o
press "Home Folder" to insert the path to the folder where TSM was started,
also called the "Start-in" folder.
Press OK to confirm the change, or Cancel.
The file categories are:
*Results...
This folder holds the automatic results window listing enabled by
File / Results / Enable Background Saving, and other text files,
42
also graphics files of all types.
*Data
Default location of data files.
*Model Files Temporary files, with .tsd suffix, holding data associated with
models.
*EDF Files
Empirical distribution function files in spreadsheet format, created
to provide test p-values. Typically an EDF file is associated with
a model.
*User Code Files with extension .ox, supplied by the user, to be compiled
with the main program.
*Batch Files
Code (.ox) files and output (.tsd) files generated for external
jobs, such as Monte Carlo experiments run in parallel, including
Condor jobs. These files are temporary and are normally deleted
after their contents has been consolidated.
Notes:
1.
The file locations are stored in the TSM settings file and remembered
between sessions.
2.
The same folder can be used for any or all of the file categories, By
default, this is the home folder. Using separate folders becomes the more
convenient option when large numbers of files are generated. These
locations can be subfolders of the home folder, and can also be located
elsewhere in the file system.
3.
If the model, EDF, and user code file locations are changed, the files
associated with the current program settings are moved physically to the
new locations.
4.
Data files can be loaded from anywhere, but if edited they will be saved
to the current data folder. This ensures that files read from other locations
(such as data sticks) are preserved intact by default. (They can of course
optionally be saved anywhere.)
5.
If the data file location is changed, the data file, or files, currently loaded
into TSM are saved to the new location. If the old location is the home
folder the file(s) will also be deleted from there. Otherwise it is left to the
user to tidy up the old location manually, as desired. This is to guard
against unpredictable behaviour in the event that (for example) two users
are working with a common data store.
6.
Default model, EDF and batch file locations can be set permanently by
editing the file tsmgui4. However, these default locations must be within
the home folder. Files can be stored anywhere, but locations outside the
home folder can only be set dynamically.
43
3. Setup
3.1 Setup / Set Sample
Select the sample for estimation and other data analysis procedures using the
scrollbars. Date information is given if provided with the data. The maximum
sample is selected by default.
Notes:
1.
Seven different sample selections can be set concurrently, for different
program functions. This dialog is accessible from within every dialog
where a sample must be specified, and the sample to be selected
depends on where it is opened from. The locations are
Setup / Recursive/Rolling Estimation .
.
Sample 1
Setup / Summary Statistics .
.
.
Sample 2
Setup / Nonparametric Regression .
.
Sample 3
Setup / Semiparametric Long Memory .
.
Sample 4
Setup / Cointegration Analysis .
.
.
Sample 5
Model / Linear Regression .
.
.
Sample 1
Model / Dynamic Equation .
.
.
Sample 1
Graphics / Show Data Graphic .
.
.
Sample 6
Setup / Data Transformation and Editing
.
Sample 7
Options / Simulation and Resampling . .
Sample 8
When this dialog when opened from the menu bar, it's function
depends on which dialog is currently open. By default, it sets
Sample 1.
2.
Sample selection 1 is displayed on the status bar. Sample selections
2-7 are displayed at the top left of the relevant dialogs. Sample
selections 1, 3, 4, 5 and 6 are stored as part of a model, and
retrieved by reloading the model. Selections 2, 7, and 8 are saved
with general program settings.
3.
By default, the chosen sample is automatically truncated to exclude
missing observations (denoted NaN) of any variable in the model
specified. Remember that missing values are created by taking lags,
leads and differences. The actual sample used is the sequence of
non-missing observations that terminates with the last non-missing
observation of the selected sample. Note that this is not necessarily
the longest available set of non-missing observations.
4.
Use the "All Available Observations" button to check for missing
observations. The largest sample available for all the variables in the
currently specified model is selected. The actual sample used for
estimation is restricted to this set.
5.
The sample count is initialized at the first line of the data file, not the
first available (i.e. non-missing) observation.
6.
Click the "Simulate" button if the sample is being set for a simulation
44
run, not for estimation. In this case, the "Available Sample" to be
checked corresponds to included regressors only, ignoring the
'dependent' variable to be simulated.
*
The button is highlighted when the option is selected. Cancel
it by clicking again, or by closing the dialog.
*
The button is disabled unless the dialog is opened from either
the menu bar or one of the Model dialogs.
7.
Check the "Filter Out Missing Observations" checkbox to create the
sample by simply dropping any missing observations from the chosen
interval, rather than looking for a consecutive non-missing sequence
as described in 3. This setting is in most cases inappropriate for time
series, and is disabled if any time-series model features are selected.
8.
In panel data models, the setting in this dialog determines the time
periods to be included in the estimation or simulation for each of the
individuals in the sample. The number of individuals to be included
can only be changed by editing the grouping indicator in the data
file.
9.
The sample can be specified arbitrarily by means of an indicator
variable. The indicator variable must have the name "!selectobs!"
and is applied as follows:
*
Any non-zero value: observation included in sample,
*
Zero: observation omitted from sample.
This variable can be created using the option Edit / Set Sample
Indicators in the Setup / Data Transformation and Editing dialog.
Alternatively, any existing data series can be designated as the
indicator by simply renaming (a copy of) it as !selectobs!.
Note:
*
When !selectobs! exists in the data set, a checkbox is
displayed in this dialog, to select/deselect its use.
Otherwise the checkbox isd hidden
*
The indicator is not named explicitly in variable lists.
To remove it, use the Set Sample Indicators option as
described, and change all zeros to non-zero values.
*
Only one indicator named !selectobs! can exist in a data
set at one time. Maintain two or more by assigning them
different names, and use the Edit / Rename function to
activate and deactivate.
3.2 Setup / Data Sets
By default, the program holds one data set at a time. Loading a new data set
causes the currently held data set to be removed.
Selecting the option "Load Multiple Data Sets" in Options / General (requires
a program restart to activate) allows data sets to be retaned in memory and
rapidly swapped. When a new file is loaded, the current data set is moved to
a holding area ("in the background"). It is moved back to the "foreground", for
45
analysis either by selecting it using the menu (see below) or automatically, by
loading a model which specifies it. The data set currently in foreground
takes its place in the holding area. The stored data sets are remembered
between sessions and reloaded at start-up, provided the disk files containing
them have not been moved or deleted.
Switch To... Opens a popup menu with the list of data sets held in background
memory. Click a name to bring the selected data set to the
foreground for analysis. The data set currently in foreground (if
any) moves to the background.
Note: This menu is also opened by the "Open File" button on the
tool bar. When "Load Multiple Data Sets" is disabled, this button
opens the popup menu for disk file access.
Remove...
Opens a popup menu with the list of data sets in background.
Click a name to remove the data set from memory.
Remove All Removes all data sets from memory.
New Data
Clears the foreground data space, moving the current foreground data
set to the background.
Notes:
1.
Data sets must have unique names corresponding to the name of the file
containing them, excluding the extension. It is not possible to load files with
the same name simultaneously, even if they have different extensions (file
types) or reside in different directories. A warning is shown, and unless the
action is cancelled the new data set will overwrite the existing one.
Tip: to avoid a clash, save the current data set with a new name before
opening its namesake.
2.
Use the New Data command to allow a new data set to be created in the
Setup / Data Transformation and Editing dialog. This command is available
in the menu whether or not "Load Multiple Data Sets" is enabled.
3.
When the New Data and Remove All commands are given, all menu items
and toolbar buttons that operate on data are disabled.
4.
The Switch To... and Remove... popup menus include the name of the
foreground data set in disabled (grayed out) mode. Clicking this item has no
effect. Remove the foreground data set using the New Data... command.
5.
Clearing a data set does not delete the disk file. The data can be reloaded at
any time.
6.
When the File / Settings / Export... command is given, all the currently stored
data sets are saved in the specified settings (.tsm) file. Opening this file will
cause the data sets contained in it to be re-loaded. They are written to
individual files in the working directory, using the currently selected data file
46
format.
7.
By default, a maximum if 20 data sets can be stored at one time. Change this
default by editing the tsmgui4.h file (see Appendix B).
3.3 Setup / Data Transformations and Editing
In this dialog, data series can be edited, renamed, deleted, and created as
dummies or by transformations of existing variables. The data can be rearranged,
sorted, reversed and written to new files. Observations can be pasted from
external sources via the Windows clipboard.
*
Commands selectable from the pull-down menu are arranged under the
headings "Edit" and "Transform".
o
Press a button to bring up the desired list of choices.
o
Choose the desired operation or transformation.
o
Where appropriate, select one or more variables from the list.
o
Press "Go" to execute the command.
*
Press "List/Edit Series to view and/or edit observations in spreadsheet
format, after selecting one or more variables from the list. Alternatively,
double-click the selection. This option is also available (without the
variable selection option) through the menu item
Setup / Data Spreadsheet... See 3.4 for further details.
*
To mark a variable, highlight it and press "Mark". To remove the mark,
press "Mark" with no variable highlighted. Marking enables operations
involving a pair of variables.
*
"Select All" highlights the whole list, "Clear" removes all highlights.
*
The "Sample..." button brings up the sample selection dialog. Editing
operations and transformations are performed for the selected subset of
the data, where appropriate.(This option is not available for panels.)
*
The "Formula..." button opens a text field where a formula for a new
variable can be entered directly using the notation described in 1.5.
This option is also available through the menu item Setup / Make Data
Formula... See 3.5 for further details.
*
If changes are made, the "Save Modified Data" button is enabled. Use this
to open the choice box for saving, either to the original file or as a new
file.
EDIT COMMANDS
Note: commands marked with * do not operate on individual variables.
Simply press 'Go' to execute. Any highlights in the variable list are ignored
in these cases.
47
"Rename"
After selecting a variable and pressing 'Go', a text field appears for typing the
new name. The dialog is frozen until 'OK' or the [Enter] key is pressed to
complete the entry. If multiple variables are highlighted, each is presented for
renaming in turn.
"Delete"
A confirmation box appears. Press the 'All Selected' button to delete all
highlighted variables at once, otherwise each is presented in turn for
confirmation.
CAUTION! This command cannot be undone.
"Edit Description"
Allows optional description(s) of the selected variable(s) to be created or
edited. View these descriptions in Help / Data Descriptions.
NOTE: If the total length of the name + description string (including separator
character) does not exceed 64 characters, the string is stored in the name field
of the data spreadsheet file. If this limit is exceeded in one or more cases, only
the truncated strings are saved with the data. The complete strings are saved to
a text file with matching name and extension ".names.txt".
"Save Selected"
Allows a subset of the variables to be saved in a new named file. Highlight
any number of variables in the list before giving the command. This opens
the file dialog for saving, provide a new name and type for the file. The
existing data set is unaffected.
"Make Seasonals" *
For frequency N, create N dummy variables with every Nth observation
= 1, otherwise 0. Set N = 4 for quarterly data, N = 12 for monthly, etc.
"Move Up", "Move Down"
Use these commands to re-order the variables in the data set. Pressing "Go"
repeatedly will move a single highlighted variable up or down as many
positions as required. Alternatively, move a block of highlighted variables
with a single command, but in this case the highlighting is cleared for all but
the last.
"Resize Sample" *
Use this command to create additional space for data to be entered by hand,
or created by simulation. Type the desired number of observations into the
text box provided.
*
If this number is less that the number of observations already existing,
the sample is trimmed to the specified length.
CAUTION: Excess observations are deleted, this operation is not
reversible.
*
If the number is greater than the current length, existing series are
extended with NaN values. A new variable "Zeros" is created
automatically with the full number of observations, with value 0.
Notes:
1.
Use Zeros as the dependent variable when specifying a model for
48
2.
simulation, renamed as required.
If the data set is initially empty when this command is given (give the
command File / Data / Clear to clear the current set) the new data
set receives the associated file name 'newdata ' with the currently
selected file type.
"Set Sample Start" *
Either trims the number of observations specified from the start of the sample,
or creates new rows (set to .NaN) if the number specified is negative. In the
latter case the option allows the data set to be extended manually with new
initial observations.
CAUTION: this operation is not reversible.
"Delete Selected Rows"
This command deletes complete rows from the data matrix for which the
the selected variable equals the constant entered in the box. The constant
value can be .NaN, to delete all rows where the selected variable is missing.
E.g., to extract the observations for a particular quarter from a quarterly
data set, create seasonal dummies and delete the cases where the dummy
for the chosen quarter is 0.
CAUTION: this operation is not reversible. Be careful to save the
reduced data set under a new name!
"Make Zeros", "Make Intercept", "Make Trend" *
These commands create dummy variables. Intercept has values 1, Trend
has values 1,2,3,...,T for a sample of T observations.
Notes:
1.
To create an event dummy, first create Zeros, then edit it observation
by observation in List/Edit/Compare.
2.
Use the built-in intercept and trend dummies for estimation wherever
possible.
"Make Normal(0,1)", "Make Student t(df)" *
Uses the built-in random number generator to create series of independent
observations with the specified distribution.
"Make PDL"
Creates polynomial distributed lag variates (see main document for details)
for highlighted variable(s), with lag length specified by the scroll bar. Five
new variables are created, corresponding to terms of order 0 up to 4 in the
lag polynomial. Delete any unneeded cases.
"Make .NaN"*
Creates an empty variable into which data can be entered in the editing
spreadsheet. Useful for importing a new variable, in conjunction with the
clipboard pasting option.
"Reverse Data" *
Operates on the whole data set, listing the observations in reverse order.
"Sort Data By" *
49
Operates on the whole data set, sorting the observations according to the
ascending order of the highlighted variable. Don't select more than one If two or more are selected, only the last choice is effective.
"Undo Sort" *
Reverses the action of the Reverse Data and Sort Data By commands,
restoring the data set to its original order.
"Shape"
Re-assembles, by rows, a data series of length T into c columns of length
ceil(T/c), where c > 1 is selectable. In case T is not divisible by c, the
columns are padded to equal length with zeros, and then with NaNs to fill
the rest of the data matrix.
Uses for Shape include the following:
1
Separate the real and imaginary components of a discrete Fourier
transform. Set c = 2.
Note: the jth periodogram point, for j = 1,..., [T/2], is the
sum of squares of the jth row elements of these columns.
2.
Separate seasonal data into its seasonal components. For example,
with quarterly data, set c = 4. If the first observation is from Quarter
1, then the first column created will contain the Quarter 1
observations, the second column the Quarter 2 observations,
and so on.
"Vectorize Columns"
Arranges the selected variables (two or more) into a single column by
stacking the transposed rows. The new variable is saved to a file.
For example, use this command to create a single series from a table of
monthly observations where the columns contain observations for each
month and the rows correspond to years.
Note: Use "Shape" to recreate the original table.
"Set Sample Indicators"*
Opens the data editing dialog showing a variable "!selectobs!" which
initially has all observations set to 1. Change a value to 0 to indicate that
this observation should be omitted from the estimation sample. If
an indicator set already exists, this command allows it to be edited.
Note:
1.
Once this option has been selected, an indicator variable named
"!selectobs!" is saved with the data set, and is enabled on reloading. It can be edited in a spreadsheet program if desired.
2.
The indicator does not appear in the variable list, but its
values are displayed in the editing dialog following the
observation numbers/dates.
3.
To use the sample indicators, check the checkbox in
Setup /Set Sample. (This checkbox is hidden unless
indicators exist.)
"Set Dates" *
Allows the dates of observations to be set or changed. This works exactly like
the method for inserting date information into a data file prior to loading;
50
see File / Data. for details. A new column of the data set is created with name
!STARTDATE!, and opened for editing. Enter the initial year in the first row,
the initial sub-period in the second row, and the sub-period frequency in the
third row. Enter 2 for half-years, 4 for quarters, 12 for months, etc.
Notes:
1.
The new column is deleted immediately after the new information is
processed.
2.
The date information is saved with the data in GiveWin or other
spreadsheet formats, and also in ".dat" files, although not in matrix
(.mat) files.
3.
CAUTION! This operation is not reversible. If the observations
are already dated, the existing date information will be lost, including
individual daily dates.
4.
If the period is set to 0, the series is treated as undated. Observations
are numbered from 1.
"Set Date Labels" *
A variable with the reserved name "!DateLabels!", is created if it does not
exist, and opened for editing. Enter the required date labels for each row of
the table. Arbitrary numerical values are allowed. This variable is not
displayed in the variable list, but appears in the Date column in the data table,
taking precedence over Ox-format Year-Period dates. To reinstate the latter,
give the "Set Dates" command, as above.
CAUTION: Calendar date information will be deleted permanently.
"Print to Results Window"
This command allows observations to be cut and pasted into other
applications. Variables are listed in single columns, even if two or more are
selected. Use the Sample dialog to select the required range, before giving
this command.
TRANSFORM COMMANDS
*
*
*
*
*
*
Most commands in this menu can also be executed using the Edit / Make
Formula command. Here, they can be performed with a single click on
any number of highlighted variables.
Created series is/are added to the end of the list, with a self-explanatory
prefix or suffix appended to the name(s). Use Edit / Rename to change
the automatically created name, if desired. Use Edit / Delete to remove
any unwanted series.
Xt, t = 1,...,T denotes a highlighted variable in the data set.
Mt, t = 1,...,T denotes the 'marked' variable, if any.
j represents the scrollbar setting for leads/lags/differences.
C, d, E, Lamda represent values entered in the text field.
"Lag"
.
.
"Lead"
.
"Difference" .
.
"Log-Difference"
.
"% Difference"
"Fractional Difference"
.
.
.
.
.
.
Xt-j
Xt+j
Xt - Xt-j
log(Xt) - log(Xt-j)
100.(Xt - Xt-j)/Xt-j
Sum{i=0,...,t-1}Bi*Xt-i, where Bi =
Gamma(i-d)/(Gamma(d).Gamma(i+1))
51
"Cumulate" .
.
.
"Logarithm" .
.
.
"Exponential".
.
.
"Logistic"
.
.
.
"Log-Odds" .
.
.
"Square"
.
.
.
"Square Root"
.
"Reciprocal" .
.
.
"Power"
.
.
.
"Sine" .
.
.
.
"Cosine"
.
.
.
"Absolute Value"
.
.
"Max(X,C) (C#Marked)"
.
"Min(X,C) (C#Marked)"
.
"Sign"
.
.
.
"Add C (C#Marked)".
.
"Subtract C (C#Marked)" .
"Multiply by C (C#Marked)"
"Divide by C (C#Marked)" .
"Centre (Mean-Devs)"
.
"Standardize" .
.
.
"Detrend"
.
.
.
"Moving Average" .
.
"Fourier Transform" .
.
"Hodrick-Prescott Filter"
.
"Cubic Spline"
.
.
"Principal Components"
.
“Reverse Series”
.
.
Sum{j=0,...,t-1}Xt-j
log(Xt)
exp(Xt)
exp(Xt)/(1 + exp(Xt))
log(Xt/(C - Xt)) (C = 1 or 100)
Xt^2
Xt^(1/2)
1/Xt
X^E (E an integer), |Xt|^E (otherwise)
sin(Pi*C*Xt)
cos(Pi*C*Xt)
|Xt|
max(Xt, C) (max(Xt, C*Mt))
min(Xt, C) (min(Xt, C*Mt))
+1 if Xt >= 0, -1 otherwise
Xt + C (Xt + C*Mt)
Xt - C (Xt - C*Mt)
Xt*C (Xt*C*Mt)
Xt/C (Xt/(C*Mt))
Xt - Mean(X)
(Xt - Mean(X))/SD(X)
Xt - a - b*t (by regression).
j-point moving average.
See 8. below.
HP filter with penalty Lamda
Cubic spline, see 9 below.
PCs of the selected variables.
Time reversal.
Additional Notes:
1.
By default, missing observations resulting from forming lags, leads or
differences are replaced by NaN, and these rows are omitted from
estimation automatically. Select the "Pad with Zeros" radio button to
replace with zeros instead, so that the rows are retained for estimation.
2.
Note that when leads or lags are created, the excess observations are
not discarded. The end (start) of the complete data matrix is extended
with extra rows, the missing observations being filled with either NaNs
or zeros, depending on option selected.
3.
If a sub-sample is selected using the "Sample..." button, the excluded
observations are set to NaN in the new series.
4.
NaN is returned in the case of illegal values (e.g., negative arguments
of log(.) and (.)^(1/2), x < 0 and x > C in log-odds.)
5.
The 'Power' transformation returns the power of the absolute value for
non-integer exponents. The square root transformation is an alternative
way to take the power of 1/2, but behaves differently, assigning NaN
to negative observations.
52
6.
The symbols # and % are used in the new variable names to denote
multiplication and division in variable names. The more logical choices
'*' and '/' cannot be used in file names.
7.
"Moving Average" creates the MA of series coordinates from lag 0 to
lag j-1. To create a centred moving average, set j to an odd value and
apply the (j-1)/2-point "Lead" transformation.
8.
"Fourier Transform" computes the FFT of the selected series. The real
and imaginary parts of the transform are vectorized to give a real series
of the same length of the original, with cosine and sine terms alternating.
The components can be separated again if required, using Edit / Shape.
Note: The series as generated are of length 2T, and are trimmed to fit
the existing data set. To avoid losing these points, first extend
the data set using Edit / Re-Size Sample.
9.
Set the cubic spline bandwidth to zero for the default setting. Positive
values represent the number of parameters used in the fit, so larger
values yield a closer fit to the data - matching the sample size yields
a perfect fit.
For irregularly spaced observations, use Mark to select the variable
containing observation dates, before giving the command.
3.4 Setup / Data Spreadsheet
WINDOWS IMPLEMENTATION
The command opens a new dialog in spreadsheet format, allowing individual
observations to be viewed and edited.
The List/Edit dialog provides a simple spreadsheet-style editing interface.
*
To select a cell, click with the the mouse or use the navigation keys
(Enter, Arrows, Page-Up, and Page-Down).
*
To edit the contents of a cell "in place", double-click the cell to open
for editing. Click a second time to highlight the contents.
o
To discard the edit and retain the existing value, press
the "Escape" key.
o
To change the cell contents, press any navigation key or
select another cell with the mouse.
*
Alternatively, press 'Edit Observation'. The value in the currently
selected cell appears highlighted in the Edit box. Type the new value.
Then press:
o
'Next' (or the [Enter] key) to save the new value, move the
highlight to the next observation, and load this for editing.
o
'Copy' to save the new value, move the highlight to the next
observation, but retain the new value in the Edit field.
o
'Cancel' to discard the new value and close the Edit box.
*
To paste one or more data values from the Windows clipboard into
cells in a column, select the first cell in the range and press the
"Paste Clipboard" button, or enter the keyboard command Ctrl-V.
Press Close, or the [X] button, to close the editing dialog.
53
Notes:
1.
The left-hand column shows row numbers and dates, and is readonly. These cells cannot be selected or edited.
2.
Editing "in place" may round the data value to fit the cell - six
significant digits is the maximum. If precision is an issue, the 'Edit
Observation' text field allows exact editing of the value, with up
to 12 digits retained after the decimal point.
3.
Use the Copy button to repeatedly insert the same value to successive
observations. This option allows easy creation of (e.g.) dummies for
sub-periods.
4.
Observations can be copied via the Windows clipboard from sources
such as text editors, word processors, spreadsheet programs and the
TSM results window. The clipboard must contain a character string
consisting of data values and separators (files cannot be pasted)
*
A data value is a string containing digits 0-9, optionally a
decimal point (.) optionally starting with a minus (-), and may
include an exponent with the form "e+nnn" or "e-nnn" where
"n" denotes a digit and "E", "e" are equivalent.
*
A separator may consist of any number of arbitrary characters
except 0-9 and ".-+eE". Spaces, tabs, punctuation marks
(except ".") and carriage returns are all eligible separators.
For example: a variable listed by observation in columns (to be read
left-to-right and down, a common format) can be copied complete to
the clipboard and then pasted into a column of the table, appearing in
the correct order.
5.
If the number of pasted values exceeds the number of available rows in
the spreadsheet, the excess values are discarded. Remember that the
spreadsheet dimensions match the sample selected for editing, not
necessarily the full data set.
6.
CAUTION: Editing cannot be undone! To undo edits, re-load the
original data file.
LINUX/AWTJAPI IMPLEMENTATION
This menu item is disabled in this implementation. Series can only be listed
from the Setup /Data Transformation and Editing dialog.
In the List/Edit dialog, a listing of the first selected series appears, with
observation numbers/dates.
*
Use the 'Mark' button to compare two series. If this command is
given for a variable while another is marked, the two series are listed
side by side.
*
To edit an observation, either double-click it, or highlight and press
'Edit Observation'. The existing value appears highlighted in the Edit
field. Type the new value, then press
o
'Enter' (or the [Enter] key) to save the new value, move the
highlight to the next observation, and load this for editing.
o
'Copy' to save the new value, move the highlight to the next
observation, but retain the new value in the Edit field.
o
'Cancel' to discard the new value.
Press Close, or the [X] button, to close the editing dialog, or,
54
Press >>>>> or <<<<< to list the next/previous series in the data set.
Notes:
1.
Use the copy button to repeatedly copy the same value to successive
observations for (e.g.) easy creation of dummies for sub-periods.
2.
The marked (right-hand) series cannot be edited.
3.
CAUTION: editing cannot be undone.
3.5 Setup / Make Data Formula
This command gives direct access to a text box where formulae can be
entered to create new variables as functions of existing variables in the data
set.
The formula should be typed in the box in the format
[New Variable] = [Formula]
where [New Variable] represents a variable name and [Formula] represents text
formulated as described in Section 1.5, 'Entering Formulae' (Case A).
Notes:
1.
These actions can also be performed as an option in the dialog Setup /
Data Transformation and Editing - press "Formula".
2.
If [New Variable] matches an existing variable in the data set, a choice
box is displayed with the option to over-write it. Otherwise, the new
variable is added to the data set.
3.
Variables can be referenced either by name or in the format X[j]
where j denotes the column number in the data set. These numbers
are displayed in the variable list in Setup / Data Transformation and
Editing when this option is accessed there, as noted in 1. Be
careful not to overlook that these numbers may change, relative to
the corresponding names, if variables are deleted and/or
re-ordered. Reference by name is the safer option, especially when
stored formulae are re-evaluated after data modifications..
4.
To evaluate a recursive formula, use E#{-j} to denote the function
value lagged j periods.
By default, zero initial values are assigned to E#{-j}. To assign
different start-up values do as follows, assuming the recursion
contains M lags.
1)
Create a new variable with the name to be assigned to the
formula.
2)
Edit this series, as necessary, so that the desired start-up
value(s) appear in the M initial positions.
3)
Press "Sample..." and advance the initial date for the
calculations by M steps.
4)
Create the formula, selecting "Yes" when prompted to
overwrite the series.
5)
Reset the initial date to view the complete series in the
55
spreadsheet, including the start-up values.
5.
If the formula as entered cannot be parsed, an error message appears
and nothing is changed.
TEXT BOX CONTROLS
"Close"
Closes the text box.
"Delete"
Deletes the currently displayed formula, the clears field.
"Next"
Displays the next formula, if it exists.
"New"
Opens a new blank formula where there is no "Next".
"Previous"
Displays the previous formula, if it exists.
"Go"
Creates new variable from the displayed formula.
[Return]
Equivalent to pressing "OK".
[Escape]
Discards current editing, restores existing formula.
Closing the text box with the Windows Close button [x] is equivalent to
pressing "Cancel".
"Run All"
Evaluates all the currently stored formulae in sequence.
The button bar also displays a formula number (i) in the format [ i / n] where n
denotes the number of formulae currently stored.
3.6 Setup / Automatic Model Selection
Two options for estimating a sequence of models automatically are controlled
from this dialog. Note that they cannot be run simultaneously.
AUTOMATIC REGRESSOR SELECTION
When this option is selected in the Actions menu, or by pressing the "Run
Regressor Selection" button, the program chooses the set of regressors to
optimize the chosen model selection criterion, out of the specified regressors
in a baseline model. The option is described in detail in 6.4 Actions /
Automatic Regressor Selection. Use the checkboxes in this dialog to choose
which regressor 'Types' are to be included in the initial set to search over.
For example, select 'focus' variables (to be included in every specification)
as Type 1 regressors, and 'nuisance' variables, whose inclusion is optional,
as Type 2 regressors. To conduct the search over the latter set only, uncheck
the box "Include Type 1 Regressors" and check the box "Include Type 2
Regressors".
Notes.
1.
To set the selection criterion (one of Akaike, Schwarz and Hannan-Quinn)
open Options / Tests and Diagnostics, and select the radio button under
"Model Selection Criterion".
(This setting is also used for choosing lag lengths in ADF cointegration tests
and Saikkonen-Stock-Watson efficient estimation.)
2.
Tip: to make the lags of a focus (Type 1) variable optional, set Type 1 lags
to 0, and then create the one-period lag in Setup / Data Transformation and
Editing. Include this variable as a Type 2 with Lags set to the desired
maximum.
56
3.
A confirmation box opens to guard against accidental launches. This reminds
you what selection criterion is currently chosen.
MULTIPLE ARMA MODELS
When this option is selected in the Actions menu, or by pressing the "Run
Multiple ARMA" button, the program automatically estimates all the ARMA(p,q)
or ARFIMA(p,d,q) specifications, for all values of p and q in the indicated
ranges.
*
Enter max p, max q and max p+q in the text fields provided. With the default
settings (all entries = 2) the program estimates the following cases of (p,q), in
the order shown: (0,0), (1,0), (2,0), (0,1), (1,1), (0,2).
*
A confirmation box appears to guard against accidental launches.
*
See Actions / Estimate Multiple ARMA Models for additional details.
3.7 Setup / Recursive/Rolling Estimation
This dialog sets up the options for recursive estimation. For details on the output
produced by this option, see Contents / Actions Menu / Recursive/Rolling
Estimation.
*
Choose rolling estimation (fixed sample size) or incremental estimation
(extending sample size) with the radio buttons.
*
Set the initial sample in the usual way, as for the estimation sample.
Access the Set Sample dialog either using the button provided, or in
Setup / Set Sample or in a model dialog.
*
The 'Go' button duplicates the Actions Recursive/ Rolling estimation button.
If this dialog is open, the "Run" button on the toolbar is a third way to
launch the run. A confirmation box opens to guard against accidental
launches.
Notes:
1.
'Step size' is the number of extra observations added at each step. Set by
dragging the scrollbar. If this setting is greater than 1 the sequences of
estimates are plotted as step functions.
2.
The terminal observation required will in most cases be the maximum
available. The scrollbar allows it to be set smaller. The lower limit is
constrained by the initial sample and step size settings.
3.
The first check box allows the option of saving regression diagnostics and
test statistics to be selected. This is on by default.
4.
The second check box allows saving to a file of all the forecasts for each
estimation period.
NOTE: The forecasts, other than the N-step-ahead, cannot be displayed
57
interactively.
5.
By default the number of forecast steps (N) is fixed, and the N-step
forecast is reported for each recursion step. If the second check box is
checked, the terminal forecast date is fixed, so that N contracts as the
end of the sample advances. This option can be used to compare the
forecasts of a particular date from different standpoints.
3.8 Setup / Compute Summary Statistics
This dialog presents the variable list. Select one or more variables and press 'Go'
to print tables of summary statistics. Alternatively, just double-click a variable.
Optionally, the following tests for integration order are computed:
Tests of I(0)
*
The Robinson-Lobato (1998) nonparametric test of I(0)
*
Lo's (1991) R/S test for I(0) against I(d), for d > 0 or d < 0. A bounding
p-value (probability of the statistic exceeding the computed value under
H0) is given in braces.
*
The Kwiatkowski et al. (1992) (KPSS) test of I(0), against I(1). A
bounding p-value (probability of the statistic exceeding the computed value
under H0) is given in braces.
*
The Harris-McCabe-Leybourne (2006) N(0,1) test of short memory (see
8.2 Options / Tests and Diagnostics for additional details.
Tests of I(1)
*
Phillips-Perron (1988) test of I(1) against I0). A bounding p-value (probability
of the statistic lying below the computed value under H0) is given in braces.
*
The augmented Dickey-Fuller test of I(1) against I(0). The number of lags is
chosen to optimize the Schwarz criterion over the range 0 to [T^1/3].
*
Elliott-Rothenberg-Stock (1996) GLS-DF test of I(1)
*
Elliott-Rothenberg-Stock (1996) P (feasible likelihood ratio) test of I(1).
Robinson's (1994) semiparametric estimator of d is also computed. See Robinson,
Anns. Stat. 22, 515-539. The statistic corresponds to eq. (4.2) of the paper with
lamda_m = 2 pi n^{-0.35} and q = 0.5.
Notes:
1.
Check the 'Detrend?' box to compute the statistics for the series after
detrending by OLS.
2.
Check the 'Differenced?' box to compute the statistics for the differenced
58
series in addition to the undifferenced series.
3.
Choose the order of correlograms of the series and squared series, with
associated Q statistics, using the scroll bar. If this is set to 0, no
correlograms are computed. Choice of Box-Pierce or Ljung-Box Q test
variants is selected in Options / Tests and Diagnostics.
4.
Check the "Data Correlations" checkbox, with Correlogram Order set to 0,
to see the contemporaneous correlation matrix of two or more series.
In this case, no other statistics appear, and the I(0) and I(1) test
checkboxes are "grayed out". If only one series is selected with this option
set, no output is produced.
5.
Check the "Data Correlations" checkbox with Correlogram Order set to
a positive value to compute the correlograms and cross-correlograms of a pair
of series. Denoting the selected variables as 'X' and 'Y' respectively, the four
columns of the table show, for lags j > 0:
*
The autocorrelation sequences Corr(X_t, X_t-j) and
Corr(Y_t, Y_t-j)
*
The cross-correlation sequences Corr(X_t , Y_t-j) and
Corr(Y_t , X_t-j)
Note that stationarity is assumed so that Corr(X_t, Y_t+j) is taken to
be the same as Corr(Y_t, X_t-j).
6.
Check the "Partial Correlogram" checkbox to print the partial autocorrelation
functions (PACF) instead of the simple autocorrelations.
7.
Optionally, the number of correlogram and partial correlogram points plotted
in Graphics / Show Data Graphic can be controlled by the setting in this
dialog. Check "Make Graph Order" to enable this feature.
8.
Check the "Quantiles" checkbox to report the following quantiles of
the data distribution: 0.01, 0.05, 0.1, 0.3, 0.5, 0.07, 0.09, 0.95, 0.99.
For small samples the extreme cases are omitted.
*
Note that if detrending is specified, the mean of the distribution
is zero by construction.
9.
The "Sample..." button opens a dialog to set the sample period to be
analysed (Sample 2). See Setup / Set Sample for details.
10.
The test p-values are computed from the published tables and are not
available for every ordinate. The values given are upper bounds.
Dickey-Fuller's table for the maximum sample size is quoted for the
ADF and Phillips-Perron tests, and in this case the probabilities refer to
the lower tail.
11.
The settings for the various order tests (bandwidth/kernel/ ADF lags)
are selected in the dialog Options / Tests and Diagnostics. Note that
the lags are chosen automatically using a model selection criterion
unless the "No Criterion" option is selected.
59
3.9 Setup / Nonparametric Regression
Opens a dialog to specify a Nadaraya-Watson estimate of the conditional mean,
using the Gaussian kernel. Two variables must be selected from the list, the
dependent variable y and regressor x. Use the radio buttons to toggle between
these choices.
Press "Sample ..." to open the Set Sample dialog and select the sample to be
analysed (Sample 3). This sample is shared with the semiparametric long
memory estimators, and can be set in either dialog.
By default, the bandwidth used is S.n^{-1/5} where n = sample size and S is
the sample standard deviation of the regressor. Use the scroll bar to increase
or decrease this setting by factors of 2.
The function is plotted with the y-x scatter optionally superimposed.
3.10 Setup / Semiparametric Long Memory
This dialog computes estimates of the long-range dependence parameter d, using
one of three semiparametric methods:
*
"Narrow-band" log periodogram regression (Geweke and Porter-Hudak,
1983) The log-periodogram points for j=1,...,M are regressed on
-2log(sin(pi.j/T)) where T is sample size, and M/T --> 0.
*
"Broad-band" log periodogram regression (Moulines and Soulier, 1999)
The log-periodogram points for j=1,...,[T/2] are regressed on
-2log(sin(pi.j/T)) and P Fourier terms (cosine functions of pi.j/T) to
approximate omitted short-range components, where P --> infinity but
P/T --> 0.
*
Local Whittle Gaussian maximum likelihood (Kunsch 1987, Robinson 1995)
Maximizes the frequency domain Gaussian likelihood as function of d, using
the first M periodogram points where M/T --> 0.
The outputs from this option includes point estimate, asymptotic standard error and
t-test of significance. The log-periodogram regression methods also optionally
returns a Hausman-type test for the presence of bias (Davidson and Sibbertsen
2009). To enable this option go to Options / General / Special Settings and set
"Log-periodogram Bias Test" to TRUE (double click the text field).
Notes:
1.
To run the estimation, select a variable or variables from the list, and press
Go. Multiple selections are permitted, and will be computed in succession.
Alternatively, just double-click on a variable in the list.
2.
The series may be either differenced, or detrended by regression, prior
to computing the periodogram. Choose option with the radio buttons.
3.
Press "Sample ..." to select the sample for estimation (Sample 3). This is
stored independently of the sample selection for other program functions,
60
but is shared with Nonparametric Regression, and can be set in either
dialog. See Setup / Set Sample for details.
4.
For the GPH bandwidth and trim options, and MS Fourier terms, the
power of T being selected (to nearest integer below) is shown as a guideline.
Note that the optimal bandwidth is typically a power of T times a constant
factor, that may be small. The weight here is 1.
5.
The GPH bandwidth setting is chosen with the scroll bar GPH recommended
M = O(T^(1/2)). The minimum MSE setting is known to be M =
O(T^(4/5)), but the bias can be large with this choice. Experimentation is
recommended to see how sensitive the estimate of d is to the selection.
6.
The GPH trimming option also omits the lowest frequencies. See the relevant
literature for guidance on this setting. If in doubt, keep at 0.
7.
The bandwidth used to compute the GPH bias test (see Davidson and
Sibbertsen 2006) should be set to the maximum (T/2) to test the hypothesis of
a pure fractional process. Use this setting if in doubt. Setting the bandwidth to
CT^beta for 4/5 < beta < 1 yields a test of a more general hypothesis, allowing
any short-run dependence that does not induce bias. Note that the test is
inconsistent with beta <= 4/5.
8.
The choice of MS Fourier order is also a trade-off between bias and
efficiency - see MS paper for recommendations, or experiment.
9.
The smoothing option, available for both estimators, uses local nonoverlapping averages of periodogram points in the regression. If in doubt,
keep this setting at 1.
10.
To do Monte Carlo experiments on the estimators specified in this dialog,
have the dialog open when the model is stored in the Model Manager, or
with Model / Save Current Model...
3.11 Setup / Cointegration Analysis
This dialog allows a Johansen-type multivariate cointegration analysis to be
carried out on any subset of the data. The available procedures are:
*
Testing hypotheses of I(0) and I(1) on the selected variables.
*
Lag length selection for the Johansen CIVAR, by Akaike, Schwarz or
Hannan-Quinn selection criteria.
*
Johansen maximum eigenvalue and trace tests for cointegrating rank.
*
Wald tests of structural exclusion restrictions on the cointegrating vectors,
including MINIMAL analysis.
Select the variables to be included and CIVAR options, then select the desired
procedure using the radio buttons. To execute the procedure press Go, or the
61
Run or Evaluate buttons on the tool bar.
Notes:
1.
Open the Set Sample dialog using the "Sample ..." button to set the desired
sample (Sample 4). This selection is independent of those set for other
program functions. See Setup / Set Sample for details.
2.
The KPSS test of I(0) and P-P test of I(1) are also available in the Setup /
Summary Statistics dialog, but here, for convenience, are computed for all
the selected variables at once.
3.
The p-value inequalities reported are taken from the tables of the eigenvalue
and trace tests in Osterwald-Lenum (1992)
4.
A check box allows the inclusion/exclusion of drift terms in the CIVAR.
If the drift is suppressed, intercepts of the estimated cointegrating vectors can
be computed. However, note that standard errors are not computed for these.
5.
If the 'Drift' option is selected, a chi-squared statistic for the significance of
the drift is reported following the maximal eigenvalue and trace tests. The
degrees of freedom are p - r where p is the dimension of the cointegrating
VAR. (See e.g. Davidson (2000) Section 16.4.3 for details.)
Note: that this test is only valid if the cointegrating rank is actually equal to
r, the row of the table in which the statistic appears.
6.
MINIMAL analysis is described in Davidson (1998a). A sequence of
chi-squared tests is computed to estimate the set of 'irreducible'
cointegrating relations (such that cointegration is not a property of any subset
of the included variables.) Identified, structural cointegrating relations must
belong to this set. If the cointegration hypothesis is not rejected, estimates
of the vectors are reported, with asymptotically valid standard errors, and
Phillips-Perron statistics for the corresponding 'cointegrating residuals'.
7.
There is the option to specify a single test of the hypothesis that the
cointegrating space contains an element subject to specified zero restrictions.
When the radio button for this option is selected, the variable list shows only
the currently selected CIVAR variables. Select a subset of these to test the
hypothesis that they form a "cointegrating subset".
8.
Scroll bars allow setting the number of additional lags in the CIVAR, and also
the cointegrating rank to be assumed for computing the 'beta' matrix of
cointegrating vectors. This setting is taken as given in the MINIMAL analysis.
9.
See Davidson (1998a) for details of the "rule of thumb" adjustment to the
chi-squared critical values.
3.12 Setup / Monte Carlo Experiments...
This dialog provides the options to set up and run one or more simulation
experiments. To make use of it, there should normally be at least one model
62
stored using the Setup / Model Manager dialog. If two different models are
stored, one can be used to generate the artificial data and the other to specify
the estimation, allowing a flexible approach to misspecification analysis.
*
Select one or more Data Generation Models (DGMs) from the list
*
Select one or more Models for Estimation (EMs) from the list (can be the
same as or different from the DGMs).
*
Use the scroll bar to select the number of replications, and set other
options with the checkboxes.
*
Press "Run" to perform the experiment(s). To interrupt a run in progress,
press the "Stop" button on the toolbar, with the options of aborting or
continuing.
*
Press "Clear Models" to clear all highlights from the model list.
*
Press "Results" to
o
Re-display the tables from the experiment last run with the
currently loaded DGM.
o
Load and display Monte Carlo results from file, including batch
output.
Notes:
1.
The model list can be rearranged, and also sorted alphabetically, in the
Model Manager (see Section 4.1).
Note: When the model list is sorted, block selection by dragging or
right-clicking the mouse (see Section 1.4) is disabled.
2.
Multiple experiments can be set up by selecting two or more models in
either category.
o
If one EM is selected and two or more DGMs, then the experiment
is performed on the EM using each DGM in turn.
o
If two or more EMs are selected and one DGM, then the experiment
is performed on each EM using the specified DGM.
o
If multiple models are selected in both categories, then all the possible
experiments are performed - each DGM with each EM in turn.
o
The same model(s) can be selected in both categories.
3.
In a single experiment, if "Run" is pressed a second or further time without
changing any run settings, the option is presented to add further replications
(the number currently selected). If the last run was aborted, then the options
of either resuming or extending the last run are presented similarly.
This feature is not available when multiple experiments are specified.
4.
The sample period for estimation is always defined by the DGM. The sample
settings for the EM are ignored. To have a dynamic simulation run for a
number of start-up periods, select the "Presample Data Random in
Simulations" option in Options / Simulation and Resampling. Then set the
DGM sample period as desired for estimation.
63
5.
If no models are defined, the current specifications are stored as a model with
the default name (run ID) and used for both DGM and EM.
6.
The DGM specification MUST include a choice of shock distribution
(Gaussian, Model or Bootstrap) selected in the Options / Simulation and
Resampling dialog. Set the shock variance in the same dialog for the Gaussian
option, and appropriate parameter values in the Values dialogs for the Model
option. Make these selections before saving the DGM.
7.
Between 1 and 1 million replications can be specified. The selectable values
are in the ranges 1,2,..,5,10,...,50, 100,...,1000, 1500,...,10000, 15000,...,
100000, 150000,...1000000.
8.
If a test takes a variable parameter, such as degrees of freedom or
number of tested restrictions, the tables display this value enclosed in
square brackets appended to the test name. The suffix is omitted if the
parameter has a default value, such as 1 in the case of t-ratios.
OPTIONS:
9.
The parameter moments reported are the mean, standard deviation,
skewness and kurtosis of the Monte Carlo distribution of parameter
estimates.
10.
Optionally, moments can be computed for the estimated standard errors
of the estimates, using whatever formula is specified in the EM (standard,
robust or HAC). The mean of this distribution may, for example, be
compared with the SD of the Monte Carlo distribution of the estimate.
11.
To calculate parameter biases and RMSEs, the assumed "true"
parameter values must be set as part of the EM. These may match those
of the DGM, but note that the two models need not even be comparable.
Set these values for unconstrained parameters using the Values dialogs in
the usual way.
Note: this option is not available for semiparametric long memory
estimation, which does not make use of the Values dialog. The bias and
RMSE can be hand-computed from the information reported in this case.
12.
Any optional tests that are specified in the estimation model will be
included in the tabulations. The routinely computed diagnostic tests
(Jarque-Bera test and Q tests) can be optionally included in the
tabulations. By default, they are omitted.
13.
The upper-tail quantiles of the distributions of the test statistics (50%,
10%, 5%, 2.5%, 1%) are optionally reported in the case of parameter t
values. By default, the absolute t values are tabulated, so that, for example,
the 5% tail quantile should be approximately 1.96 in large samples when
the null hypothesis is true.
14.
Also optionally reported are the empirical distribution function (EDF)
points for the nominal p-values. If the test criteria are correctly sized,
64
these distributions should be Uniform [0,1] if the null hypothesis is true,
and 100x% of replications should lie below x. Over-rejection yields a
value larger than the nominal one. The cases tabulated are x = 0.01,
0.025, 0.05, 0.1, 0.5.
15.
The option "2-sided" causes the p-value EDF to be computed for the
upper and lower tails combined, as well as the upper tail. For example,
in the case "5%", the reported value is the fraction of p-values in the
replications falling outside the equal-tails range of [0.25, 0.975].
When combined with signed t-statistics (see next paragraph) this option
gives a result comparable to tabulation of the absolute t-statistics, but
differing in the case of asymmetry about zero. It also shows the
coverage probabilities for any user-defined statistic.
16.
Optionally, the signed t statistics can be tabulated instead of the absolute
t statistics, to allow the evaluation of one-tailed tests. In this case, the 5%
tail quantiles should be approximately 1.64 in large samples when the null
hypothesis is true. Note that the upper tail is tabulated, so be sure the
parameters are signed appropriately.
17.
The t statistics can optionally be centred on the parameter values specified
by the EM (see para. 11 above). Otherwise, they are centred on 0. When
this option is selected with the EM and DGM values matching (as when
the same model takes both roles) the distributions of the test statistics can
be studied under the (true) null hypotheses.
Note: this option is available only when the bias and RMSE are available.
18.
When the distribution of test statistics follows the distribution specified for
the null hypothesis, the p-values should be uniformly distributed, so that their
c.d.f. is the 45-degree line of the unit square. The Kolmogorov-Smirnov
statistic (the maximum absolute difference between the p-value EDF and the
uniform distribution) can optionally be calculated. This provides an alternative
to the quantiles to assess how closely the distributions match.
Nominal critical values for the K-S distribution, assuming 80+ bins, are
1.22 (10%), 1.35 (5%), 1.63 (1%).
Note: this option is only available if the frequency table is enabled, see
para. 20 below.)
19.
If GMM is simulated, there are two options available, the "one-step"
estimator, and the efficient GMM estimator using the first-round estimates
to compute the weight matrix. Check the "iterated GMM" checkbox to
select the latter option. Further iterations are not possible, in this release.
20.
If "Print Model Descriptions" is checked, the complete non-default model
settings are printed in the output. These are codes in the TSM scripting
language, see the Programming Reference document for details.
Note: Thee same lines appear in the model description field in Model
Manager, if "Automatic Descriptions" is checked when the model
is saved. However, they are generated independently and do not
need to exist in the stored model.
65
21.
By default, the individual replications are stored. These can be plotted as
kernel densities or histograms (see Graphics menu) , or written out to a
spreadsheet file for further analysis using Files / Listings / Save MonteCarlo
Replications. For 1000+ replications, the option Save Frequency Table
is enabled, together with a field to enter the desired number of bins for
histogram construction. This option results in the actual replications being
discarded. The distribution of the first 1000 replications is used to
construct the data range and bin widths for construction of the frequency
table, given the number of bins selected. As well as putting no constraint
on memory for large experiments, this option also allows higher quality
graphics, with control over the smoothing bandwidth for kernel density
estimation.
22.
Increasing the number of bins used to generate the frequency distributions
gives more accurate estimates of quantiles and test sizes, at the cost of
greater computing time. The default setting of 100 gives sizes estimated to
the nearest percentage point.
23.
Check the "Save EDFs" checkbox to save tabulations of the empirical
distribution of test statistics. If the t statistics are centred on the true
parameter values, or otherwise if the null hypothesis of interest is set to be
true in the simulation, these distributions can be used to provide critical
values, and hence to estimate true test powers by simulating cases of the
alternative. These tables can also be used to generate p-values for tests in
observed data.
24.
EDFs are saved as spreadsheet or matrix files of the type specified by
Options / Output and Retrieval / "Export Listings to Files of Type". The
assigned file names are of the form "EDF_Run" + run i.d. + extension.
These files can be renamed, merged and/or edited either in TSM or a
spreadsheet program (see below). See Appendix G for details of the
EDF file format.
Note: The prefix "EDF_" is recommended for file names, since such
files can be loaded easily by drag-and-drop.
OUTPUTS
25.
The results of the experiment, including tables and plots data, are
automatically stored with the DGM at the end of the run. Reloading this
model allows the tables (using the "Results" command) and graphics to
be re-displayed at any time. When performing a sequence of
experiments, save the DGM under a new name before modifying or
re-using it, so as to preserve these results for future study.
26.
The complete set of replications (or the frequency table if this option is
selected) can be also exported to a spreadsheet file for further analysis.
Give the command File / Listings / Export Spreadsheet / Monte Carlo
Replications. The distributions can also by displayed graphically.
The command Graphics / Monte Carlo Distributions opens a dialog to
select and display the empirical densities of each parameter, test
statistic and p-value. These are optionally displayed in both histogram
and kernel density form. The normal curve with matching mean and
66
variance can be optionally superimposed for comparison; see
Options / Graphics.
27.
See 7.3 Graphics / Monte Carlo Graphics for further information about
creating plots, including the ability to combine density plots from different
experiments, for comparison.
RUNNING AN EXTERNAL PROCESS
28.
Check the "Run as External Process" checkbox to launch the run as a
batch job in a console window. This option allows the TSM GUI to
remain under the user's control for other tasks while a long Monte Carlo
job is performed. A temporary executable Ox file is created to be run
in batch mode in a console window. The file has the generic name
"Batch_Run[ID].ox" where [ID] denotes the run ID number. The file is
deleted at closedown if "Delete Temporary Files on Exit" is checked
in Options / General.
29.
When the run is completed, the results are sent to a text file with the
generic name "Batch_Run[ID].txt". This can be loaded in the TSM
window using the command File / Load Text File.
Note:
*
The listings for the run are stored with the Data Generation
model. Reload this model to see the plots.
*
If "# Parallel Runs" is set to 1 or greater the action is different,
see 31ff below.
30.
If the checkbox "Defer External Jobs" is checked in Options / General,
the Ox file containing the job is created, but not started automatically.
Use this option if the job is to be run at a different time or on a different
machine, for example.
CONDOR
31.
If running on a network with the Condor HTC system implemented,
the procedure for launching a Condor job is effectively the same to
processing on the local machine, as described above. Simply check the
"Run Condor Job" checkbox, when this is displayed. Like external jobs
to be run locally, Condor jobs can be either started from within TSM,
or deferred to be launched manually. See Appendix H for information
on working with TSM in the Condor environment.
32.
Condor can optionally copy the Ox files needed to run the jobs from
a different Ox installation. The obvious application here is where the
user is running the 64-bit versions of Ox and TSM under Windows,
while the Condor cluster consists of 32-bit workstations. Then, the
files need to be taken from a 32-bit Ox installation. Set the item
'Condor Alternative Executable' to TRUE to enable this option, and
then enter the path to the Ox installation as a text string in 'Condor
Executable Path'. For the case given, the entry required would typically
be "c:\program files (x86)\oxmetrics7\ox\". (Type without the quotes.)
33.
Condor will optionally return files after a run containing diagnostic
67
information. These include log files generated by Condor itself, and also
the standard output that would appear in the DOS console window if
the job were running locally. To switch on the writing of these files, go
to Options / General, Special Settings, and set either or both of
'Condor Log Files' and 'Condor Output Files' to TRUE (equivalently,
enter 1 in the text field). To switch off the outputs set the relevant fields
to FALSE (equivalently, enter 0).
PARALLEL PROCESSING
34.
A batch job consisting of a single experiment can be divided up into
several runs in parallel, according to the setting of "# Parallel Runs".
This feature allows a dual core or quad-core processor to be exploited
to speed up the run time of the experiment two-fold or four-fold.
The executable files in this case receive the generic names
"Batch_Run[ID]_Inst??.ox", where [ID] stands for the run ID, and ??
denotes the instance number. The instances can also be run on different
machines. One way to do this is to check "Defer External Jobs" in
Options / General, and copy and run the Ox files by hand. On a network
with the Condor environment installed, parallel processing on multiple
machines proceeds automatically, "as if" being run on the local machine.
35.
When the runs are completed, the outputs from each instance are written
to temporary files with names matching the Ox files and the ".tsd"
extension. Press the "Results" button, choose "Load Results from File"
and select any file called "Batch_Run[ID]_Inst??.tsd" in the file dialog.
The complete results for the runs are automatically imported and
aggregated into a single set of tables for display. The option is presented
to save the aggregated results in a new ".tsd" file and delete the individual
instance files (".ox" and ".tsd"), in addition to output and log files if these
have been created.
Note:
*
There is no need to wait for all the instances to complete to
perform the aggregation step. Select the highest-numbered file
to be sure that all those available are loaded.
*
However, don't choose the temporary file deletion option until
all instances are returned! Aggregation must be done as a single
operation.
*
An alternative way to load the batch outputs is by the command
Files / Tabulations / MC Batch Results..... Or, in Windows,
simply drag any of the files to the results window with the
mouse.
*
An alternative way to save the aggregated results is by File /
Listings / Save Listings File...
36.
By default, the instances return the actual replications. Sorting and
frequency calculations are done at the aggregation stage. This exactly
replicates the procedure for a single run, and is recommended for most
purposes. High-quality plots are available with this option provided
the total number of replications, in all instances, is at least 1000.
If the option "Save Frequency Table" is set (only permitted with at
least 1000 replications per instance) the frequency tables returned by
68
each instance are simply averaged. This method is appropriate where
each instance involves a large number of replications, and the minor
distortion induced by averaging can be tolerated. (Note: bin widths
for sorting are chosen dynamically and may differ slightly across
instances).
37.
To ensure the parallel experiments are statistically independent of each
other, each is supplied with a different seed for the random number
generator. If the current seed is S, the seed sent to each instance is
calculated as floor(M*U[0,1]), where U[0,1] is a uniform random number
generated successively for each instance, using S, and M = 2147483647
is the largest positive integer available in Ox. In the case where the seed
is user-supplied (see Options / Simulation and Resampling), this scheme
ensures reproducibility of the complete parallelized run. By default, S
is generated from the system clock as the number of seconds since
midnight.
WARP SPEED BOOTSTRAP
38.
When this option is turned on, bootstrap tests are computed by doing just
one bootstrap replication in each Monte Carlo replication. The p-values
are then computed by locating the sample statistics in the distribution of
bootstrap statistics over the experiment.
39.
To activate this option, go to Options / General / Special Settings, scroll
to the bottom of the choice list and double-click the text field to change
the toggle setting. Set the bootstrap options as usual for the model for
estimation, but remember that the "Bootstrap Replications" setting is
ignored. Also note that the actual replications must be recorded to
construct the bootstrap distribution when the experiment terminates,
hence the "Save Frequency Tables" option is also ignored.
3.13 Setup / Tail Probabilities and Critical Values...
This dialog gives access to tabulations and plots of standard distributions:
the standard normal and Student t, either signed or absolute, and the chisquared and F distributions.
*
Select the radio button for the distribution required.
*
Set degrees of freedom as appropriate (except for "EDF from File",
see Note 4 below).
*
Depending on the dialog opened, enter either the critical value to get
the tail probability, or the tail probability to get the critical value.
*
To show the probability/critical value (also printed in the results window)
press the right-hand button. To plot the density with the tail area shaded,
press the left-hand button.
69
Notes:
1.
The "tail probability" is the area of the upper tail of the density, to the
right of the critical value. Use the critical value to perform a 1-tailed
test with the corresponding significance level.
2.
The distributions "|Normal|" and "|Student t|" allow calculation of p-values
for 2-tailed tests. These correspond to the p-values reported with the
estimation output.
3.
Use the signed distributions "Normal" and "Student t" to calculate p-values
for 1-tailed tests. Just cut and paste the test statistic into the "Look Up Tail
Probability" dialog. Change its sign for tests of the lower tail.
4.
Select "EDF from File", then press "Select", to choose a test statistic
from the currently open EDF file - the file dialog opens automatically
if no EDF file is currently open. To open a different EDF file, use
the command File / Data / Load EDF.
5.
The density plot is the same in either dialog. The shaded region is the
area corresponding to the tail probability, and equivalently, the area to
the right of the critical value.
3.14 SsfPack State Space Modelling
Note: This option needs SsfPack 2.2 to be installed. See Appendix A
for details.
This dialog sets up models for estimation and evaluation using the "SsfPack
Basic 2.2" suite of state space functions. For information on the model options
and interpretation of the outputs, consult the SsfPack documentation.
Univariate models can be constructed and estimated by maximum likelihood
using the SsfPack routines for ARMA and unobserved component models.
In addition, models can be formulated by constructing the state space
matrices directly using the handy matrix editor. In the latter context both
univariate and multivariate models can be handled, although not estimated.
Model specifications and estimates can be stored and retrieved using the
Model Manager, in the same way as for regular TSM models. Model outputs,
including state and signal predictions and forecasts, conditional means and
standard deviations, smoothed states, disturbances and simulations are written
to the data matrix, for display using TSM graphics or for further analysis.
*
The 'Show >>>' button opens/closes the matrix editing box. Select the
matrix to be displayed in the adjacent choice widget (pull-down menu).
*
The 'Values' button opens a dialog to display and edit model
parameters, and set parameter fixes and bounds. See Section 5.0 of
this manual for information on the options in this dialog.
*
The 'Parameter Constraints' check box enables the estimation of models
subject to constraints, and also the calculation of Wald and LM tests of
70
specified constraints. The adjacent square button opens the Model /
Constraints dialog. See Section 4.9 of this manual for information on the
options in this dialog.
*
The 'Clear' button resets all model settings and variable selections.
*
The 'Sample' button opens the sample selection dialog.
*
The 'Select Task' pull-down menu allows selection from the range
of Ssfpack operations available on the specified model.
*
The '<<< Go >>>' button executes the selected task.
*
The 'Save Data' button writes the data set to a file. This button is
enabled following a task that adds new series to the data set.
MODEL COMPONENTS
The three radio buttons allow selection of variable(s) for analysis, regressors and
state space components. Select/deselect variables and components by clicking
items in the lists.
Notes:
1.
At least two model components (from the set Level, Slope, Seasonal,
Cycle and Irregular) must be selected. The Slope component can only
be selected if Level is also selected.
2.
Only one of the seasonal model options can be selected at a time. The scroll
bar setting fixes the seasonal frequency in conjunction these options,
otherwise it has no effect.
3.
Trigonometric seasonals are available in two forms, either constraining the
variances of the trigonometric components to be equal (=) or allowing
them to be different (/=).
4.
The parameters of the unobserved components/ARMA model are identified
in the Values dialog and outputs in the results window by a naming scheme
based on the following identifiers. Multiple cases (e.g. cycles, intercepts,
lags) requiring numbering have the appropriate suffixes appended:
Shock variance:
Level .
.
.
Slope .
.
.
Dummy seasonal
.
Trigonometric seasonal
Harrison-Stevens seasonal
Cycle .
.
.
ARMA
.
.
Irregular
.
.
Cycle frequency:
.
.
Cycle damping factor: .
.
.
.
.
.
.
.
.
.
.
.
71
.
.
.
.
.
.
.
.
.
.
SgLevel
SgSlope
SgSeasD
SgSeasT
SgSeasH
SgCycle
SgArma,
SgIrreg
Lamdac
Rho
ARMA lag coefficients: .
.
Signal-noise ratio (cubic spline) .
State intercept:
.
.
Measurement intercept:
.
5.
.
.
.
.
.
.
.
.
AR, MA
q
InterceptD
InterceptC
The state space ARMA coefficients and shock variance share storage
spaces with the same parameters in conventional TSM dynamic equation
models. It is accordingly possible to formulate and estimate an ARMA
equation in the Dynamic Equation dialog, and then move with these
estimates direct to the state space framework for prediction or
filtering, or to be incorporated into a new model.
MODEL DIMENSIONS
The scroll bars allow the setting of AR and MA orders, the seasonal frequency
and the number of post-sample forecasts to be computed.
6.
If no model with preset features and estimable parameters is specified,
the "State Vector" scrollbar is enabled allowing the manual formulation
of a state space model of the indicated dimension. If any model features
are selected, this scrollbar is disabled.
MATRIX EDITING
A state space model is defined by up to seven matrices, which can be either set
up by the predefined SsfPack functions and parameter values, or entered
directly in the editing box.
Following the notation in the SsfPack documentation, these matrices (with
dimensions indicated, where m = number of states and n = number of variables)
are
*
Phi
.
.
.
transition matrix
(m + n) x m
*
Omega .
.
.
variance matrix
(m + n) x (m + n)
*
Sigma .
.
.
initial state
(m + 1) x m
*
Delta .
.
.
intercepts
(m + n) x 1
Indicators for time varying components of Phi, Omega and Delta, having the
same dimensions, are J_Phi, J_Omega and J_Delta. These matrix elements,
when present, are set either to -1 or to a number indicating the column of
the regressor matrix containing the requisite time varying component.
Note: The regressor matrix is assembled from the selected columns in the
variable list in the same order as they appear there.
Select the matrix to be edited (or simply inspected) from the pull-down menu,
then either press 'Show >>>' or double-click the menu itself.
*
After opening, the editing box can be re-sized by dragging the corners
with the mouse.
The editing options are as follows:
*
Double-click a cell to open it for editing.
*
Press the Enter key - OR click anywhere else in the table - to save
changes to a cell.
*
Press the Escape key to discard changes to a cell.
*
Press 'Clear' to change all cell entries to 0.
*
Press 'Paste' to paste the contents of the clipboard into the matrix.
72
*
*
*
Press 'Print' to have the matrix appear as text in six-column format in the
results window.
Press 'Code' to send the matrix to the Results window in Ox format, for
pasting into an Ox program.
Press 'Close' - or press the 'Show >>>' button again in the main dialog to close the editing box. If it has been edited, a prompt to save or
discard the changes appears before closing.
Notes:
7.
The Paste operation fills the cells in a left-to-right-and-down mode from
the contents of the clipboard, starting at the currently selected cell. Only
numerical values (including signs, decimal points and exponents written
as "eXX" ) are pasted. Punctuation, spaces, carriage returns and other
non-numeric characters, are all ignored. If the entries overflow the available
cells, they are discarded.
To see the capabilities, try the following:
o
Write the matrix with 'Print'.
o
Clear the box with 'Clear'.
o
Now copy the printed matrix to the Windows clipboard,
select the top left cell, and press 'Paste' to restore it.
8.
If no preset components selected, saving the matrix increments the Run ID
value. Otherwise, the Run ID is incremented only by running the maximum
likelihood algorithm.
TASKS
The pull-down menu 'Select Task' gives access to the following SsfPack
functions, which are called with the currently specified state space matrices,
dependent variable(s) and regressors as arguments. The corresponding
SsfPack function name and mode are indicated in the right-hand column.
"Evaluate Likelihood"
.
.
"Maximize Likelihood"
.
"Maximize Profile Likelihood"
.
"Likelihood Grid Plot"
.
.
"Prediction and Forecasting" .
.
"Conditional Means, States/Signal "
"Conditional Means, Disturbances" .
"State and Signal Smoothing"
.
"Disturbance Smoothing " .
.
"Standardized Smoothed Disturbances"
"Simulation from State Space Model"
.
.
.
.
.
.
.
.
.
.
.
SsfLik(...)
SsfLik(...)
SsfLikConc(...)
SsfLik(...)
SsfMomentEst(ST_PRED,...)
SsfCondDens(ST_SMO,...)
SsfCondDens(DS_SMO,...)
SsfMomentEst(ST_SMO,...)
SsfMomentEst(DS_SMO,...)
SsfMomentEst(DS_SMO,...)
SsfRecursion(...)
Notes:
9.
Selecting the option "Fit Variances in Logs" is generally recommended for
efficient likelihood maximization, and allows zero to be the natural default
starting value in in model estimation. If this option is not set, the default
starting value for variances is automatically selected as unity.
10.
The "profile likelihood" option concentrates out the variance of the irregular
component, thereby reducing the dimension of the parameter space. When
73
this option is selected, the corresponding parameter is removed from the
parameter vector for iteration, and the solved value appears separately in
the output.
When an ARMA model is specified without an irregular component, the
ARMA shock variance is concentrated out.
11.
All Tasks except those involving likelihood evaluation/optimization result in
generated series being written to the data set. These series are identified by
coded mnemonics, as follows, as well as a Run ID usually relating to the
last likelihood optimization.
PrdSt .
.
.
State predictions
PrdMs .
.
.
Measured variable predictions
FrcSt .
.
.
State forecasts
FrcMs .
.
.
Measured variable forecasts
U_st .
.
.
Disturbances, states
U_ms .
.
.
Disturbances, measurement eqn(s).
sU_st .
.
.
Standardized disturbances, states
sU_ms .
.
.
Standardized disturbs., measurement eqn(s).
MnSt, SmoSt .
.
Conditional means, states
MnMs, SmoMs
.
Conditional means, measured variables
DsSt .
.
.
Disturbance means, states
DsMs .
.
.
Disturbance means, measured variables
SimSt .
.
.
Simulation of states (Gaussian shocks)
SimMs .
.
.
Simulation of measured variables
(Gaussian shocks)
12.
A prefix "sd" attached to any of the above mnemonics indicates the
corresponding series of standard deviations, where these are computed.
Note that SsfPack returns variance series. TSM takes the square roots
for reporting purposes so that they may be used directly in the construction
of confidence interval plots. To do this, use the Multi-Series Plot 'C-Bands'
option in Graphics / Show Data Graphic... (See Help page 7.1, under
Multi-series Plotting.)
13.
The "standardized disturbances" are ratios of disturbances to the
corresponding standard errors, as reported by SsfPack, to allow
tests for outliers and breaks.
14.
The "Conditional Means" and "Smoothing" tasks actually return the same
series, although computed by different methods (functions SsfCondDens
and SsfMomentEst respectively) the former being evidently the more
numerically efficient, although the latter function computes the variance
series as well as the mean series. In spite of this, the mean series are
given different identifiers (with "Mn" and "Smo" prefixes respectively)
so that the outputs from these two functions can be distinguished.
15.
If the 'Extended Output' checkbox is left unchecked, only the series
relating to measurement equations are written. Check this option to get
the full reporting of series for both state and measurement equations.
16.
The 'Forecasts' scroll bar setting determines the number of post-sample
74
forecasts to be generated under the "Prediction and Forecasting" task.
If set to zero, only in-sample predictions are returned. If the post-sample
period extends outside the range of the data set, additional rows are
added to accommodate it.
17.
Unwanted model outputs created by these procedures, in the form of
columns added to the data matrix, are easily deleted in the Setup / Data
Transformation and Editing dialog. However, since large numbers of
outputs can be generated in models with many states (e.g. with seasonal
components) it is recommended to create a dedicated data file containing
only the series for analysis. Do this using the "Save Selected" option in
the same dialog. This file could then be deleted at the end of the analysis
without touching the original data store.
18.
NOTE: Errors in SsfPack routines are not generally trapped! In some
cases they may even lead even to the termination of the Ox program
calling them, and hence of TSM, with an error message printed to standard
output. It is strongly recommended to enable "Error Recovery" in Options
/ General, so that error messages are accessible in the DOS box.
75
4. Model
4.0 Model / General
This page provides general information on setting up models using the set
of dialogs grouped under the "Model" menu. The "Linear Regression" dialog
controls models that are estimated by evaluation of a formula (analytic
solution of normal equations) without the need for numerical optimization.
This is also true of most of the panel data options presented in "Panel Data".
By contrast, all the methods set up in the "Dynamic Equation" dialog are
estimated numerically, although there are some cases (linear models) in
which the resulting estimator is the same.
MODEL MANAGER
Model specifications, including fitted or imposed parameter values and other
model outputs in graphical or listing form, can be stored under a supplied name,
and subsequently retrieved from a list, using the following commands in the
Model menu. More detailed control of model storage and retrieval is available
through the Model Manager dialog.
Load a Model...
Opens a pop-up menu listing models in order of last
retrieval. The default maximum number of list entries
is 20 If the model required is not on the list, access
it though Model Manager.
Save Current Model...Opens a text field where the name for the new model
can be entered. The current model name appears in the
field for editing or confirmation. If the name entered
already exists in the model list, a confirmation
box opens with options "Overwrite" and "Cancel".
Quick Model Save... Saves the current model under the current model name,
without prompting. Use this command to skip the naming
steps under "Save Current Model...".
BUTTONS
1.
The "Values" button either opens the corresponding Values dialog, or
refreshes it with new settings if it is already open. If any parameters are
"fixed" in this dialog, the button is highlighted as a reminder.
2.
The "Clear" button sets all specifications in the dialog to the defaults.
3.
The "Go" button, where provided, is an alternative way to launch an
estimation, equivalent to selecting the "Run" button on the toolbar, or the
Actions / Run Estimation menu item.
4.
Where provided, the "Sample" button opens the Setup / Set Sample
dialog.
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5.
Where provided, the "Options" button opens the last-opened estimation
options dialog from the Options menu. By default, this is the Tests and
Diagnostics dialog.
Notes:
1)
Pressing the Options button repeatedly cycles through all the
accessible options dialogs.
2)
Only relevant options are accessible from this button, depending
on whether it is located in the Linear Regression or Dynamic
Equation dialog. All options dialogs are accessible in the usual
way, through the menu or the >>> and <<< bars.
ACTIVATING SPECIAL FEATURES
The special model features specified in these dialogs (conditional variance,
supplied function, regime switching, equilibrium relations, parameter constraints)
can be turned "on" and "off" in two ways:
*
Checking/unchecking the appropriate checkbox in the main "Dynamic
Equation..." dialog.
*
Checking/unchecking the "Active" checkbox in the relevant dialog.
These pairs of switches are connected, so always show the same status
Notes:
6.
The activation status of a model feature is shown by check marks against
the menu item, as well as by the check boxes.
7.
If it is not possible to activate a feature (e.g. no options have been
selected) the "Active" checkboxes are disabled.
8.
The current model feature settings are retained even when the feature is
de-activated.
DIALOG CONTROL
All dialogs are closed when an estimation is run. Restore them to their original
positions by the Actions / Restore Dialogs command, or by clicking the
"Windows" button on the tool bar. Alternatively, select the option to have them
restored automatically following a run; see Options / General.
SPECIFYING SYSTEMS OF EQUATIONS
9.
A system of equations is specified by checking this option in the main
Model dialogs, and then selecting a set of two or more dependent variables.
All the equations are given the same specifications (AR/MA components,
regressors, etc.). The specification of individual equations is changed by
selecting restrictions on individual parameters in the Values dialogs.
10.
To modify the specification of an equation, first open the corresponding
Values dialog. Use the left and right arrow buttons at the case of the
dialog box to switch between equations. To exclude a regressor (or lag)
from an equation, select the "Fixed" checkbox for the parameter(s) in
question, and then make sure that 0 is entered in the Values field. If
desired, any other fixed value can be set.
11.
Variables selected as endogenous can also appear on the right-hand sides
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of the equations as Type 1 regressors, to allow a simultaneous system.
Three Stage Least Squares can be selected as an option in the Model
/ Linear Regression dialog. In the Dynamic Equation dialog, the presence
of such variables automatically causes the FIML estimator to be computed,
provided suitable identifying restrictions have been imposed on the equations.
See Section 4.4 for further details.
12.
Equilibrium relations can be embedded in systems of equations to create an
error correction model or cointegrating VAR. The Model / Equilibrium
Relations dialog allows the selection only of a set of variables to be
included in all the relations. The Values dialog is used to impose restrictions,
which must include a normalizing restriction (fixed at -1, typically) on one
variable.
AUTOMATIC DATA TRANSFORMATION
13.
Variables in a model may be subject to transformations. Logarithms are
the most popular case, but absolute values, squares, logistics and others
may also have applications. While one way to do this is to create and
store the new series in the database, a convenient alternative is to
perform the specified transformation "on the fly", after setting up the
equation(s) in terms of the original variables.
14.
To implement this option, go to Options / General / Special Settings
and select "Automatic Data Transformations" from the pull-down menu.
Double-click on the text field to toggle the option on and off.
15.
To indicate to the program the transformation required for each variable,
edit the data description field (see Setup / Data Transformation and
Editing / Edit / Data Descriptions).
*
The data description field should contain the flag #FN (case
sensitive) followed by the formula to be implemented, which is
written using the syntax detailed in Section 1.5, "Entering
Formulae". (This is "case E".)
*
The reserved variable names s# and S# may be used to represent
the variable being transformed, as an alternative to its actual name
which is also valid. (Note that the transformation may involve
other variables in the data set as well as constants.)
*
For example, the text
#FN log(s# + 100)
transforms the data by taking the logarithm after adding 100.
Note how spaces can be freely used to improve readability.
*
This text should follow any other material appearing in the
data description.
16.
If the transformation is 1-1 with a unique inverse, fitted values and
forecasts may be optionally reported for the original series, not the
transformed ones. To implement this option, a formula for the inverse
transformation must be provided.
*
Following formula, enter the text #INV followed by
the formula for the inverse function.
*
In this case, use either of the reserved names s# and S#
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to represent the transformed variable.
For example, the text
#FN log(s# + 100) #INV exp(s#) - 10
specifies the transformation and its inverse.
Only include this component if forecasts of the original variables
are required.
*
17.
To preserve backwards compatibility, the text #LOG (case
sensitive), appearing anywhere in the data description field,
specifies the simple logarithmic transformation and its inverse.
Thus, the strings "#LOG" and "#FN log(s#) #INV exp(s#)"
are equivalent.
CONDITIONAL VARIANCE SIMULATION
18.
If the string #CVAR appears in a variable description, followed
by the name or column number of another variable in the data set,
this is ignored unless the variable is simulated in a Monte Carlo
experiment and simulating the model in question produces a
conditional variance series, for example, a GARCH or Markovswitching model. In this case, the generated conditional variance
series is written to the column indicated. This is then available
for analysis at the estimation stage of the experiment.
4.1 Model / Model Manager
A "model" is the complete set of specifications, values and results from estimation
or simulation of an equation or system of equations. At any time, the program holds
in memory the specifications that the user has selected, and either starting values
entered, or estimated values following an estimation run. This dialog allows
model specifications and results to be stored under identifying titles, and
subsequently recalled. Material stored includes parameter estimates with information
on restrictions or bounds, estimation and testing options, generated series, forecasts,
recursive estimates and criterion plots. The latter series can be used to produce
additional plots and test statistics without re-running the estimation. Stored models
are also used to set up Monte Carlo experiments.
"Load Model"
Loads the model whose title is highlighted in the list.
"Store Current Model"
Opens a text field for the entry of a model title.
To complete the entry and store the model, either
press Return or click the "OK" button, otherwise
click "Cancel" .
"Model Description"
Opens a text box where details of the highlighted model
can be entered by the user for later reference. Click the
button again to close the box.
"Move Up"/"Move Down" Use these buttons to arrange the order of the models
in the list.
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"Sort" ("Unsort")
Sorts the model list. There is the choice of sorting by
name, and by the date of last modification (most
recent first). The "Move Up" and "Move Down" buttons
are disabled. If the list is currently sorted, the button
restores the original ordering.
(NOTE: Sorting by date is only approximate for models
created with TSM versions prior to 4.43.)
"Delete"
Opens a confirmation box, and removes the model
whose title is currently highlighted in the list if the
action is confirmed.
"Clear All"
Opens a confirmation box, and removes all models
in the list if the action is confirmed.
STORING MODELS
1.
By default, the model title "Run ###" is displayed in the text box, where ###
denotes the current run ID number. The entry can then be edited as desired.
If an existing title is first highlighted, this name appears in the text box. If
"OK" is pressed without changing it, the current specifications overwrite the
ones stored under that title. This option allows a stored model to be modified
or updated. Rename a model by loading it, saving it under the new title, and
then deleting the original copy.
2.
The Store command places the model specifications in a memory buffer, but
does not save them to disk. Give the command File / Settings / Save or Save
As... to save them permanently in a .tsm file. When a settings file is reloaded,
the stored models it contains will be accessible as before.
3.
A stored model contains the complete current settings of all model dialogs,
including Model / Linear Regression, Model / Dynamic Equation, Setup /
Nonparametric Regression, Setup / Semiparametric Long Memory and
Setup / Cointegration Analysis. For the purposes of Monte Carlo
experiments, the model is recorded as a linear regression, a dynamic
equation or a semi-parametric long memory model, depending on which
dialog is open when the Store command is given. Note that estimation is
always done numerically when launched from the Dynamic Equation dialog.
To have the desired estimator recorded as part of the stored model, have
the appropriate dialog open when the Store command is given.
4.
There is an option to store the estimated model automatically following a
successful estimation run - see Options / General. Use this option with care,
since the settings file could potentially become very large.
5.
In addition to parameter values, results and listings associated with a model
are stored in a file with the name of the model and the suffix ".tsd". These
files are not intended to be read or manipulated outside TSM. To save
results to spreadsheet files, use the commands under File / Listings. However,
note that the latter data cannot be read back into the program for purposes
such as graphing, or calculating tests.
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6.
If the Store Current Model command is given following a Monte Carlo
experiment, the replications or frequency tables (whichever have been
specified) are stored in the ".tsd" file under the given model title.
7.
If the "Store Data with Model" box is checked, a copy of the data set is
saved in the ".tsd" file. This will be loaded automatically when the model
is re-loaded. If this box is not checked, you are prompted to save the
current data file if it has been edited, and the file with this name is reloaded
with the model - however, there is no protection against it being altered in
the interim, in this case.
8.
If "Store Results with Model" is checked, the text of the last-run estimation
output is stored as a string. When the model is re-loaded, the next tile Actions
/ Evaluate at Current Values is chosen (or "Calculator" button pressed) causes
a choice box appears, presenting the option of re-displaying the results.
9.
If the "Save as Generic Model" checkbox is checked, the data file is not
reloaded with the model, which is the default action. This setting is
appropriate for models intended to be adapted to different data sets.
For example, such a model may specify inputs for a user-coded estimate
or test.
Note: If this option is selected, the "Store Data with Model" and "Store
Results with Model" options are disabled.
10.
Stored models include the current settings for the Semiparametric Long
Memory and Cointegration Analysis dialogs. Different settings for these
modules can therefore be stored and recalled in the same way as for
the main equation specifications.
11.
As models are created and modified, settings and estimates are not
discarded when specifications change -- if a regressor, or equation,
is deleted, its position in the model is recorded and it can then be
reinstated at a later stage, with the associated parameter values.
It may be desirable to delete these hidden components when the
model is finalized, to conserve memory and file space and ensure
speedy and robust processing. To finalize a model (permanently
remove unused components) Check the "Finalize Model" checkbox
before giving the command "Store Current Model". Note that the
check is cancelled automatically.
LOADING MODELS
12.
Loading a model overwrites the current settings. Store these first, if they will
be needed subsequently.
13.
See 8 above: press the "Evaluate" button to re-display the estimation output,
if this has been saved with the model. This saves time if re-evaluating the
results would be time-consuming, as when output of bootstrap inference is
selected.
14.
The data file specified in the model will be reloaded automatically, provided it
has not been deleted or moved. It can have been edited, or had series added
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to it, but any variables that appear in the model must of course be present in
the file, otherwise an error occurs. It is the user's responsibility to ensure this,
and the safest way is to check the "Store Data with Model" box so that a
dedicated copy of the data is saved.
DEFAULTS
15.
When program settings are cleared and restored to defaults, a model called
"Defaults" is created automatically. It is recommended to set up your preferred
options for routine operations, and use Defaults to store these settings. They
can then be easily restored, by loading this model.
MODEL DESCRIPTIONS
16.
When the descriptions box is open, other dialog functions are disabled.
However, the description displayed can be changed by selecting a different
model from the list. Use the PgUp and PgDn keys to scan rapidly through
the list.
17.
If the "Automatic Descriptions" checkbox is checked, non-default model
settings are written to the descriptions box automatically when the model is
stored. These are coded in the scripting language detailed in the programming
manual. This provides a convenient way to check that the model specification
is as intended.
Note: If either the Semiparametric Long Memory or the Cointegration
Analysis dialogs are open when the Store command is given, the
settings written relate to those modules; otherwise, the usual model
settings are written.
18.
You can type your own comments in the model description field. However,
these will be saved with the model only if "Automatic Descriptions" is
unchecked. To save the model settings and personal comments together,
save the model first with "Automatic Descriptions" checked, then add your
comments and save again with the option unchecked
19.
If the "Print Descriptions" checkbox is checked, the model description, if any,
is written to the results windows when the model is loaded.
DELETING MODELS
20.
When a model is deleted, the associated ".tsd" file is deleted from the disk.
Also note that these files are overwritten when a new model is stored with
the same name.
21.
There is an option to remove all the ".tsd" files automatically at shutdown.
Their contents, except for Monte Carlo results, can be regenerated by running
the command Evaluate at Current Values with appropriate options set.
4.2 Model / Linear Regression...
This dialog is for specifying a linear equation, for estimation by Ordinary Least
Squares (OLS) or Instrumental Variables (IV/2SLS). When a system of equations
is specified, it also permits estimation by the "seemingly unrelated regressions"
(SUR) and three stage least squares (3SLS) system estimators.
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*
Select the type of estimator required under Select Estimator. The options
offered depend on whether the System of Equations checkbox is checked.
For IV estimation, select the instruments in the Model / Select Instruments
dialog.
*
Variables for inclusion in the equation are chosen by highlighting them in the
list. First, use the radio buttons to choose which type variable to specify,
either the dependent variable(s), or regressors of Types 1 or 2. Any number
of regressors can be selected, of either type, but not as both types at once.
Only one dependent variable can be selected, unless the "System of
Equations" checkbox is checked.
*
Set the 'Lags' scrollbar to automatically include lags, up to the set order, of
all variables of the Type whose radio button is currently selected.
*
Use the check-boxes to include an intercept and/or a trend dummy.
*
To run a Wald test of parameter constraints, first enable this option using
the check-box. Open the Model / Parameter Constraints dialog by clicking
the square [...] button. Parameters for zero and linear restrictions must be
specified in the Values / Equation dialog.
*
To run a cointegrating regression, first enable the "Cointegrating Regression"
options by checking the checkbox.
Then:
o
check either or both of the Cointegration Test checkboxes to
compute the residual Phillips-Perron and/or augmented
Dickey-Fuller statistics.
o
Check "Fully Modified Least Squares" to compute the PhillipsHansen (1990) FMLS efficient estimator.
o
*
Check "SSW Efficient Least Squares" to compute the least squares
estimator augmented by leads/lags of regressor differences as proposed
by Saikkonen (1991) and Stock and Watson (1993) (SSW-LS).
If a panel data set is loaded, the dialog is automatically formatted in panel
mode, with the "Panel Data..." button enabled. This button opens the
Model / Panel Data dialog, which can also be accessed from the menus.
*
For Instrumental Variables estimation (IV/2SLS/3SLS), use the
"Instruments..." button to open the selection dialog.
*
The "Diagnostic Tests..." button opens the diagnostic test selection dialog, or
closes it if it is open. This dialog can also be accessed from Options / Tests
and Diagnostics. The show/hide status is remembered when this dialog is
closed and re-opened.
*
The "Sample ..." button opens the Set Sample dialog, or closed it if it is open.
Use this to select the observations to be used for estimation. The setting is the
same as if opened from Setup / Set Sample. Pressing the "Simulate" button
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allows the "All Available Observations" button to show the available sample
of exogenous variables for a simulation of the dependent variable. The
show/hide status is remembered when this dialog is closed and re-opened.
*
The "Options..." button opens the most recently opened estimation options
dialog from the Options menu. By default, this is the Tests and Diagnostics
dialog. Click the horizontal <<<< and >>>> bars in these dialogs to switch
between them.
*
The "Values..." button opens the equation Values dialog, or refreshes it if it is
already open.
*
To compute the estimates, press the <<< Go >>> button. This duplicates the
'Evaluate' button on the toolbar, and the Actions / Run Estimation menu item.
*
The "Clear" button clears all settings in this dialog.
Notes:
1.
For models specified in this dialog the estimates are computed by the
usual analytic formulae. Equations specified in the Model / Dynamic
Equation dialog are estimated by numerical optimization, whether or not
their form is linear.
2.
When this dialog is opened, the Dynamic Equation, Conditional Variance,
Supplied Function and Regime Switching dialogs are all closed
automatically. These features are all disabled ("greyed out"), until it is
closed again. All estimators except Least Squares and IV are also
unavailable.
3.
See Model / Select Instruments for details of the instrument selection
procedure.
VARIABLE AND LAG SPECIFICATION
4.
When one or more variables are selected in any category, the
corresponding radio button is highlighted (lighter grey). To see the
actual variable(s) (highlighted in the variable list) and the lag order
selected, click on the radio button in question.
5.
Regressors of Type 1 can have a different lag order specified from those
of Type 2. It is recommended to (e.g.) make variables for lagging of Type
2, and others, such as dummies, of Type 1. If lags are not specified, then
regressors of Types 1 and 2 are equivalent.
6.
In single equation mode, if the dependent variable is selected as a
regressor of Type 2, and Lags > 0, only its lagged value(s) are included
in the set. This provides an alternative way to estimate an autoregression,
without numerical optimization. In all other cases (as a regressor of Type 1,
or with Lags = 0) the dependent variable is ignored.
7.
In Equations System mode, selecting the same set variables as the
"Dependent Variables" and as "Regressors of Type 2", with k > 0 lags
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selected, results in the unrestricted VAR(k) system being estimated.
8.
The trend term, if selected with the checkbox, is a regressor of Type 1.
With this option selected, lags of Type 1 regressors are disabled to
avoid collinearity.
WALD TEST OF CONSTRAINTS
9.
Estimation subject to constraints is not available for linear regressions.
LM tests of parameter constraints and fixing restrictions are likewise
disabled, although parameters can be fixed in the usual way. However,
note that Wald and LM tests are equivalent in this case.
10.
To perform an F test of “significance of the regression”, check the Wald
Test checkbox, and also the "Test Joint Significance of Regressors" box
in the Model / Constraints dialog. Note that lagged dependent variables,
current endogenous variables in simultaneous systems and the trend term
are not included in this set by default, but can be added to it by checking
the Wald Test checkboxes in the values dialog..
COINTEGRATING REGRESSION
11.
The cointegration options are all disabled if the Systems checkbox is
checked, or the Estimator selection is IV/2SLS. The Phillips-Perron
and ADF statistics are only available with OLS estimation. These
options are disabled if FMLS or SSW-LS are selected.
12.
The Phillips-Perron test and FMLS estimator both make use of a
Heteroscedasticity and Autocorrelation Consistent (HAC) covariance
estimator. Set the desired kernel and bandwidth in Options / Test and
Diagnostics Options.
13.
The SSW-LS estimator includes leads and lags of the differences
of all variables included as Type 1 regressors. The coefficients of these
ancillary regressors are not reported in the output. Lagging Type 1
regressors is disabled. Type 2 regressors can be included, with lags
chosen by the user (not chosen automatically). For valid application
of the method, the dependent variable and Type 1 regressors must all be
I(1), while the Type 2 variables must all be I(0) (stationary).
14.
The ADF test and the SSW-LS estimator depend, respectively, on
a choice of lag length, and of lead/lag length. The lengths L can be
selected in two ways:
*
Automatically, by optimizing a model selection criterion over the
interval 0 <= L <= [n^(1/3)] . The selection criterion is is set in
Options / Test and Diagnostics. It is the Schwarz IC by default.
*
Manually, using the lag selection scrollbar. To enable this option,
set the model selection criterion to "None" in Options / Test
and Diagnostics.
15.
FMLS and SSW-LS cannot both be selected at once. Uncheck to latter to
select the former.
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4.3 Model / Panel Data...
This dialog is not accessible unless a panel data set is loaded. It sets the
available options for panel data estimation, in conjunction with settings in
the "Model / Linear Equation...", "Model / Select Instruments..." and
"Setup / Set Sample..." dialogs.
Notes.
1.
Choose the first and last date for estimation or simulation of panel
models in the Setup / Select Sample dialog. In the case of an
unbalanced panel, the first date used for a particular individual is the
later of this setting and the first available date, while the last date used
is the earlier of this setting and the last available date.
2.
The options in this dialog cannot be combined arbitrarily. When an
option is disabled or "greyed out", this means that it is not compatible
with the other current selections.
DATA TRANSFORMATIONS
See for example Arellano (2003) for details of the transformations available
here. Also note:
3.
If "Deviations from Time Means" is selected, the intercept is suppressed
automatically, if selected.
4.
The "Time Means" transformation creates a data set in which each of the
individual data points for each time period is replaced with the time
average of that individual's observations. Running a regression with these
data is identical to running a regression with the N individual means in the
case of a balanced panel. In an unbalanced panel, however, the means
effectively receive a weight Ti (number of observed periods). Be careful
to note that the number of degrees of freedom in this regression is N-p,
not O-p where O is the total number of observations (i.e. O = NT in a
balanced panel).
5.
In "Time First Differences", the first-dated observation of each individual
is set to 0.
DUMMY VARIABLES
When these boxes are checked, the corresponding dummies are created and
added to the regression. They appear in the list as regressors of Type 3.
6.
If dummies are selected in conjunction with an intercept, the first
individual/date/group is treated as the reference category, and the
corresponding dummy omitted.
7.
Group dummies are set according to the grouping indicated by the
!GROUP! guide column in the data file. If this option is selected,
the "Individual Dummies" option is automatically cancelled.
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ESTIMATOR
8.
To make use of these options, first choose "OLS/GLS" in the Model \
Linear Equation dialog. If the "IV/2SLS" option is selected, the
radio buttons in this group are disabled.
9.
GLS and ML estimators for random effects are only available for single
equations, in this release. These options are disabled if the "System
of Equations" checkbox is checked in Model / Linear Equation.
10.
The GLS and ML estimators employ the same transformation of the
data, but the parameter Tau is computed in the first case by a the
ratio of "within" and "between" regression variances, and in the second
case by an iterative procedure, using a univariate line search to optimize
the concentrated Gaussian likelihood.
11.
The text fields "SigV" and "SigEta" are provided to set up stochastic
simulations with random effects. SigV represents the within-individuals
variance, and SigEta the between-individuals variance. The contents of
these fields, which can be edited by the user, are utilized to create the
disturbances when the "Gaussian" option is selected under "Shock
Distribution" in Options / Simulation and Resampling.
Note: These values not used to initialize estimation. However, the
results from the latest GLS or ML estimation are automatically written
to these fields, as well as to the printed output, allowing an estimated
model to be easily simulated.
TESTS AND DIAGNOSTICS
12.
Standard linear and nonlinear Wald tests of restrictions on the
parameters are available for panel regressions. Choose the covariance
matrix formula, either standard or robust, in the Options / Tests and
Diagnostics dialog. The other diagnostic tests controlled from this
dialog are not available.
13.
Except in the "individual means" case, the modified Durbin-Watson
statistic due to Bhargava et al. (1982) is reported as "BFN-DW".
This provides a test for serial correlation in the within-individual
disturbances. Partial tabulations can be found in the cited paper for
the case of OLS estimation, assuming that fixed effects have been
fitted by dummies or taking individual mean-deviations. For other
cases, an EDF table might be created for statistic by Monte Carlo.
Note: in the Monte Carlo module the statistic tabulated is 2 - DW,
such that the upper tail quantiles are relevant to the positive
autocorrelation alternative.
14.
The Breusch-Pagan LM test for the null hypothesis of no random
effects is reported in OLS estimation without transformations.
This tests the hypothesis that random effects are absent. The null
distribution is Chi-squared(1) with large N.
15.
The 'variable addition' implementation of Hausman's specification
test is reported for random effects models. This tests the null
87
hypothesis that the regressors in individual mean-deviation form
are insignificant when added to the GLS-transformed equation.
The distribution is Chi-squared with degrees of freedom equal
to the number of regressors, with large N.
4.4 Model / Dynamic Equation...
This dialog sets up the specifications for a dynamic model. As well as setting the
basic ARIMA and ARFIMA specifications, as specified in equation (4.1) of the
main document, it also specifies which additional model features will be
activated.
*
Use the radio buttons to select an estimator. The estimation criteria (see
main documentation for details) are:
o
Least Squares / Least Generalized Variance / FIML
o
Instrumental Variables / GMM
o
Conditional Maximum Likelihood with Gaussian (normal) errors
o
Conditional Maximum Likelihood with Student's t errors
o
Conditional Maximum Likelihood with skewed Student's t errors
o
Conditional Maximum Likelihood with General Error Distribution
o
Whittle (frequency domain) ML with Gaussian errors
o
Probit and ordered probit
o
Logit and ordered logit
o
Poisson (count data)
o
Negative Binomial I (count data)
o
Negative Binomial II (count data)
*
Use the scroll bars to choose the order of ARMA model.
*
Use the checkboxes to select the ARFIMA (long memory) specification,
impose a unit root, select a nonlinear moving average (see 16 below) and
include intercepts of Type 1 or 2, and a trend dummy. Only one type of
intercept can be selected at a time.
*
Use the radio buttons to switch between selection of the four categories of
variable: the dependent variable, and regressors of Types 1, 2 and 3. Then
highlight the variables required in the list.
*
Set the 'Lags' scrollbar to a positive value to include lags, up to this order, of
all the variables of the Type whose radio button is currently selected.
*
Use the lower scrollbar to select the number of lags of the error to include in
the bilinear specification. If set to zero, this corresponds to the usual
AR(F)IMA(p,d,q) model.
*
Use the other check-boxes to select or deselect additional model features
(conditional variance model, coded nonlinear function, regime switching,
equilibrium relations and parameter constraints). Press the [...] button to the
left of the checkbox to open the corresponding dialog, if currently closed.
*
For Instrumental Variables estimation (IV/GMM), use the "Choose
88
Instruments..." button to open the selection dialog.
*
The "Diagnostic Tests..." button opens the diagnostic test selection dialog, or
closes it if it is open. This dialog can also be accessed from Options / Tests
and Diagnostics. The show/hide status is remembered when this dialog is
closed and re-opened.
*
The "Sample ..." button opens the Set Sample dialog, or closed it if it is open.
Use this to select the observations to be used for estimation. The setting is the
same as if opened from Setup / Set Sample. Pressing the "Simulate" button
allows the "All Available Observations" button to show the available sample
of exogenous variables for a simulation of the dependent variable. The
show/hide status is remembered when this dialog is closed and re-opened.
*
The "Options..." button opens the most recently opened estimation options
dialog from the Options menu. By default, this is the Tests and Diagnostics
dialog. Click the horizontal <<<< and >>>> bars in these dialogs to switch
between options dialogs.
*
The "Values..." button opens the equation Values dialog, or refreshes it if it is
already open.
*
To compute the estimates, press the <<< Go >>> button. This duplicates the
'Run' button on the toolbar, and the Actions / Run Estimation menu item.
*
The "Clear" button clears all settings in this dialog.
Notes:
ESTIMATION CRITERIA
1. Note limitations on the application of some estimators.
*
GARCH and Markov switching options are unavailable with least
squares and GMM.
*
Systems of equations are unavailable with skewed Student errors,
and all discrete data options.
*
The Whittle method is only implemented for univariate ARFIMA
models.
2.
If no conditional heteroscedasticity or regime-switching features are specified,
the difference between Least Squares/LGV and Gaussian ML is that in the
latter case the error variance (or covariance matrix, for systems) is estimated
jointly with the other parameters .
3.
Multi-stage GMM, with efficient weights matrix based on first-stage residuals,
is effected by running the estimation repeatedly. See Actions / Run
Estimation. For this option to be active, the type of covariance matrix
desired ('Robust', or 'HAC') must be selected in Options / Test and
Diagnostics Options. If 'Standard' is selected, only one-step GMM is
available.
4.
In the probit/logit and ordered probit/logit models, the dependent variable
must assume one of a fixed number of nonnegative integer values, including
89
0. In the standard binary case, the values must be either 0 or 1. "Count data"
are also nonnegative integers, but in this case there is no fixed upper limit to
the permitted values.
5.
To select the ordered probit/logit option, enter the number of additional cases
in the Options / ML and Dynamics dialog. Setting this value to 0 (the default)
gives the standard binary (0-1 data) cases. The data must be integer-valued
with the reference (minimum) value equal to 0, and maximum value equal
the number of cases less 1 (equivalently, 1 + the Options / ML and Dynamics
dialog entry). See Section 4.7 of the main document for the parameterization
adopted. The shift parameters are cumulated to get the total intercept shift
of each case, relative to the reference case. If an intermediate value is not
represented in the data set, the model is under-identified, but a restricted
version can be estimated by fixing the corresponding parameter to 0.
For example, if the sample data take values 0, 1 and 3, fix "Ordered probit
Gamma_2" at 0. This assigns zero probability to case 2.
MODEL SPECIFICATION
6.
Check the 'Impose Unit Root' option to estimate an ARIMA(p,1,q) model,
and also an ARFIMA(p,1+d,q) where -0.5 < d < 0.5. This option is distinct
from performing the estimation on the pre-differenced series, because the
regression statistics, plots and forecasts are all generated for the original
series of levels.
Note:
*
Any Type 1 regressors included are differenced along with the
dependent variable(s).
*
If a trend is included, it becomes in effect an intercept for the
differenced model. A Type 1 intercept is unidentified, and is not
permitted. A Type 2 intercept can enter as an alternative to the trend,
but will be suppressed if a trend is specified.
*
Type 2 and Type 3 regressors enter as usual, and are not differenced.
*
Lagged dependent variables, included as either simple regressors of
Type 2 or as components of equilibrium relations, are not differenced.
*
In fractional cointegration models, the program modifies the reported
value(s) of d3 in the appropriate way, such that 1 is added to the order
of difference d1, as reported.
7.
Use the 'Values' button to open the relevant Values dialogs, and update them
with new settings if already open. Use the 'Clear' button to remove all
selections in this dialog. The 'Go' button launches an estimation run
(duplicates the Run button and Actions / Run Estimation).
VARIABLE SELECTION
8.
The three regressor Types correspond to the vectors denoted x_1t, x_2t and
x_3t in equation (4.1) of the main document. Therefore, the estimated
coefficient of a particular regressor can be different depending its Type, when
AR and/or MA components are specified. Type 1 and 2 intercepts must be
interpreted similarly.
9.
When one or more variables are selected in any category, the corresponding
radio button is highlighted (lighter grey). To see the actual variable(s) selected
90
(highlighted in the variable list) click on the radio button in question.
10.
Only one variable can be selected as dependent, unless the "Systems of
Equations" box is checked. Multiple selection is allowed in the regressor
categories.
11.
The 'Lags' setting allows different orders of lag for the regressors of each
Type. For example, include variables for lagging in the Type 2 category, and
non-lagged variables such as dummies in the Type 1 category. Individual
lags can be suppressed by 'fixing' the coefficients at zero in the Values dialog.
If neither lags nor ARMA components are selected, and there are no current
endogenous variables, the regressor Types are all treated equivalently.
12.
If the dependent variable is selected as a regressor of Type 2, and Lags > 0,
only the lagged values are included. This provides an alternative way (from
setting AR Order > 0) of including the lagged dependent variable as a
regressor. This feature is for compatibility with the Linear Regression option.
LINEAR REGRESSION
13.
A linear equation can also be specified in the Model / Linear Regression
dialog, and in that case will be estimated by the usual analytic formulae.
Models specified in this dialog are always estimated numerically.
14.
This dialog and the Linear Regression dialog cannot both be open at once.
One is disabled whenever the other is open. The variable selections (Type
1 and 2 regressors) are common to both.
15.
An autoregression can be estimated either in this dialog, numerically, or as
a linear regression by using the Lags feature (see 5 above).
BILINEAR MODEL
16.
Remember that if the bilinear order (r) is increased from 0 to 1, this adds p
parameters to the model , where p is the AR order. However raising r further
only adds one additional parameter at each step (not p) due to the imposed
restrictions. This is different behaviour from the commonly described
unrestricted bilinear model.
NONLINEAR MOVING AVERAGE (SPS)
17.
Selecting this feature replaces the error term Ut with the expression
Ut - Ut-1(alpha + beta/(1 + exp(gamma*(Ut-1 - c1)*(Ut-1 - c2))))
where alpha, beta, gamma, c1 and c2 are additional parameters.
Combine this option with an imposed unit root to get models which can
switch stochastically between I(0) and I(1).
18.
Variants:
*
To implement a close approximation to the STOPBREAK
model, fix alpha = -2, beta = 2, c1 = c2 = 0 .
*
To obtain the STIMA model, fix gamma =100 (or any sufficiently
large value), impose the constraint c1 = -c2. Then, alpha is the
MA coefficient for small deviations (|Ut-1| < c1) and alpha +
beta for large deviations.
91
*
19.
Alternatively, all the parameters can (in principle) be freely
estimated.
Nonlinear MA models can also be implemented by coding the required
formula, see Models / Coded Equations. If both options are selected,
this one is over-ridden.
OTHER MODEL FEATURES
20.
The selectable model features are conditional variances (ARCH/GARCH),
coded functions, regime switching, equilibrium relations, and constraints.
Select these features to be included in the model with the checkboxes at the
lower left side of the dialog.
21.
If a feature checkbox is "greyed out" (disabled) this means that the feature is
unavailable with current settings, usually choice of estimator. For example,
conditional variance models need an ML estimator to be selected.
Also, "Coded Function" is greyed out if coded equilibrium relations are
specified in the Equilibrium Relations dialog. For this case the Coded
Function dialog is dedicated to specifying equilibrium relations.
22.
Model features generally require options to be set in the corresponding
dialogs to be active. It is not possible to select a feature with the checkbox,
unless some model options have been set.
23.
Click the square buttons to the left of the checkboxes to open the
corresponding dialogs. If options are set, these buttons are highlighted. The
dialogs can also be opened from the Model menu.
24.
NOTE: Values dialog(s) corresponding to model features (equilibrium
relations, switching regimes) are not accessible unless the feature is checked.
25.
To compute a Wald test as part of the run, as well as to estimate subject to
constraints, the "Parameter Constraints" box must be checked. Wald tests
can also be performed separately, see Actions / Compute Test Statistics /
Wald Test.
SYSTEMS OF EQUATIONS
26.
Select system estimation by checking the "System of Equations" checkbox.
27.
When a system of equations is specified, the estimator computed depends
on the estimator selection.
*
If the option "LGV/FIML" is selected, the log-determinant of the
error covariance matrix is minimized (Least Generalized Variance),
or FIML in the simultaneous equations case (see 22 below). In these
cases, the covariance parameters are concentrated out, and do not
appear in the vector of parameters.
*
If the option "IV/2SLS/GMM/3SLS" is selected, the estimation
method is system GMM with the instruments selected. If the
estimation is launched with the Actions / Run Estimation commands
92
or the "Run" button, the error covariance matrix set equal to the
identity matrix. However, if the command Actions / Multi-Stage
GMM is given twice in succession, the second run uses the efficient
weights matrix estimated from the current residuals. This iteration
can be repeated as often as desired. The form of the weights matrix
used depends on the Covariance Matrix Formula setting (see
Options / Tests and Diagnostics), either standard, robust (allowing for
heteroscedasticity) or HAC.
*
If the Gaussian ML, Student t ML or GED ML estimation options are
selected, the error variances and contemporaneous correlations
are estimated as additional parameters. The variances may be modelled
by ARCH and other processes by selecting the "Conditional Variance
Model" feature. These parameters (variances and correlations) can
also be subject to regime switching.
28.
If current endogenous variables are included as Type 1 regressors, the FIML
variant of the LGV and ML estimators is automatically selected. That is, the
log-determinant of the square matrix of coefficients is incorporated in the
maximand. Suitable identifying restrictions must be imposed on the
coefficients for this option to proceed. The "coefficient" of the normalized
variable in each equation is automatically fixed at 0 in this case.
Note: Endogenous variables specified as Type 2 regressors are ignored. If
lags are specified, only the lagged values are included.
29.
In a system, coded functions (see 4.6 Model / Coded Functions) may not be
simultaneous - only one endogenous variable may validly appear in each
function. However, coded functions may be embedded in linear simultaneous
systems. Note that when coded functions are specified, the residuals of these
functions replace the measured variables specified as dependent. The same
substitution also occurs if these variables appear as contemporaneous
regressors of Type I. Identifying restrictions must hold as normal.
30.
In a VARFIMA model, it is possible to parameterize the fractional difference
parameters for Equations 2,... as the differences from the parameter of
Equation 1. This makes it easy to constrain and test equality of the
parameters across equations. To select this option, set the third checkbox
in the Model / Equilibrium Relations dialog. This setting applies even if error
correction terms are not specified.
ESTIMATING TYPE I (V)ARFIMA PROCESSES
31.
It is possible to correct for the omission of the presample data in a fractionally
integrated model by including some generated regressors (depending on the d
and variance parameters). This option is enabled by setting the "Type I
Fractional" text box in Options / General to a positive integer value,
corresponding to the number of generated regressors to be included. In the
output the estimated coefficients are denoted typeIFrac-Z1, typeIFrac-Z2,....
These are akin to principal components of the omitted stochastic terms.
32.
Recommended settings are for the number of components are 1 or 2. The
columns of higher order are very small, so including too many may produce
93
unstable results.
4.5 Model / Conditional Variance...
This dialog sets up the specifications for equations (6.1)/(6.2) or equations (7.1)/(7.2)
of the main document. In the latter case, the specification set applies to the
conditional variances of each equation.
*
Use the scroll bars to choose order of GARCH specification.
*
Use the radio buttons and checkboxes to select other model options.
*
Use the radio buttons to switch between selection of the three possible types
of GARCH regressor, then click on the variable list to make the selections.
*
Distributed lags of the GARCH regressors can be specified using the 'Lags'
scrollbar, just as in the conditional mean model.
*
Check the "Abs." checkbox to take absolute values of the regressors
automatically, or the "Sq." checkbox to take the squares of the regressors.
Note that you cannot check both boxes at once.
Notes:
1.
This menu item is checked if a conditional variance model is specified. Its
settings are ignored unless a ML estimator is selected and "Conditional
Variance Model" is checked in the Model / Dynamic Equation... dialog.
2.
The 'regressor' radio buttons are highlighted (lighter grey) to show a selection
has been made.
3.
Clear all specifications with the Clear button.
4.
If the 'GARCH' radio button is selected, the 'Asymmetry' checkbox selects
the Threshold GARCH (GJR) model. In the other cases, the signed terms
of the APARCH or EGARCH are included/suppressed, depending on the
setting of this checkbox.
5.
The dependent variable(s) in the equation(s) can be chosen as GARCH
regressors of Type 2, provided the lag length is set to 1 or greater. In this
case the zero-order lag is suppressed, and the lagged dependent
variable(s) act as GARCH regressors. This is similar to the option in the
mean model. Dependent variables are NOT permitted as regressors of
Types 1 or 3. These options are cancelled automatically.
6.
If the 'Abs' checkbox is checked, the output shows the variable names
enclosed in "|" . It is recommended to check this option when lagged
dependent variables are selected, especially when running simulations.
7.
The Garch-M panel allows either the conditional variance, or conditional
standard deviation, to be added to the regressors selected in Equation…
Choose the regressor Type, and Mode, using the radio buttons.
94
MULTIVARIATE GARCH
8.
If the equation system option is selected, the default is to have fixed
correlations between the variance-adjusted residuals. An alternative is the
DCC model, in which the elements of the correlation matrix are generated
by a common GARCH(1,1)-type model. The interpretation of the
coefficients depends on the setting, standard vs. "ARMA in squares" form,
see Options / ML and Dynamics. In the first case the fitted parameters are
alpha and beta, in the second case they are delta = alpha + beta and beta.
Note:
1)
The DCC parameters are displayed in the Values / Distribution
dialog.
2)
The MA form setting in Options / ML and Dynamics does not
affect the DCC specification.
9.
If a multiple equation model is specified, the BEKK-Multivariate Garch
model can be selected. This is the case K = 1 as defined by Engle and
Kroner (1995). Be careful to interpret the parameters correctly in this
case. Selecting Equation i in the Values / Conditional Variance dialog,
using the choice widget, displays the ith columns of the Aj and Bj lag
polynomial matrices, and although note that these matrices really define the
dynamic structure of the vectorized conditional covariance matrix, Vec H_t.
See the main document for details of the model. The estimates are reported
in the results window in the same style.
Note: Neither the MA form nor the GARCH form options (Options / ML
and Dynamics) affect the BEKK parameterization.
10.
Evaluation of the DCC and BEKK likelihood functions both require
T NxN-matrix inversions, where T is the sample size and N is the number
of equations. Function evaluation could therefore be very slow for large
systems.
11.
If the BEKK option is selected, the GARCH_M variables consist of the
conditional variances and covariances of all equations. The SD mode
is not available in this case.
12.
In a system of equations with multivariate FIGARCH or HYGARCH
disturbances, it is possible to parameterize the fractional difference
parameters for Equations 2,... as the differences from the parameter of
Equation 1. This makes it easy to constrain and test equality of the
parameters across equations. To select this option (which will also apply
to VARFIMA parameters, if specified) set the checkbox in the Model /
Equilibrium Relations dialog. This works even if error correction terms
are not specified.
4.6 Model / Coded Function...
This dialog is used to set up nonlinear functions coded by the user. Coded
functions can form complete models for estimation, or components of
models. Test statistics can also be coded. See the main TSM document,
Section 4.6, for the details. The dialog is also used to specify coded
95
functions for simulated data generation.
*
Specifications created in this dialog are ignored unless the "Coded
Function" checkbox in Model / Dynamic Equation is checked.
The checkbox cannot be checked unless a specification exists.
*
The "Clear" button clears all text fields, both the parameter names
and the contents of the formula fields. Use with caution!
*
The "Clear Built-In Components" button is provided as a convenience,
for the case where the coded function represents the complete model.
Then, all other model features need to be disabled. In particular,
make sure that items such as the built-in intercept are deselected, to
avoid duplication and an unidentified model.
METHODS
There are three ways to code a model for estimation:
I.
Type coded formulae for equations or equation components into the
text box, interactively.
II.
Supply the code for the model equations as an Ox function, and
compile this with the program.
III.
Write Ox code as in II, but for the complete likelihood function.
Method I is easiest to implement, but limits the function to a single line of code.
Methods II and III allow any degree of generality, but require a minimum
of programming expertise. Since the function is compiled with the program,
TSM must be stopped and restarted to make changes to the specification.
INTERACTIVE CODING
To set up the model, do as follows:
1)
Open the Model / Coded Equations dialog, and select one of the radio
buttons "Equation", "Residual", "Nonlinear MA" and "Nonlinear ECM".
2)
Select the dependent variable(s), in the usual way, in the Model / Dynamic
Equation dialog.
3)
Type the equation formulae in the text fields. Use "Previous" and "Next"
to navigate the fields, "Clear" to initialize the formula and "Cancel" to
discard changes and revert to the stored text.
4)
Press "Test" to check the model parses OK, and list the parameter
names in the name fields below.
Notes:
1.
See Section 1.5 (General / Entering Formulae) for detailed
instructions on entering codes into the text field.
2.
Parameters removed from the equation are not deleted
automatically, but are 'suspended'. Clear the name field manually to
delete a parameter permanently from the model.
3.
Increase the 'Maximum Parameters' value and refresh the dialog to
display additional fields.
96
TYPES OF FORMULAE
"Equation"
The equation is entered explicitly, in the format " = [Formula]",
where the formula corresponds to the explained part of the
model, and implicitly the dependent variable named in the
heading appears on the left of the "=". The residuals
(corresponding to the function f1(.) in equation (4.29) of the main
document) are computed as the difference between the left- and
right-hand sides of the equation. Use this style whenever the
model can be represented in the form required - which is most cases.
"Residual"
Enter an expression which itself equates implicitly to the residuals
of the model (f1(.) in equation (4.29)). In this case, no "=" sign
should appear in the formula. The purpose of this option is to
allow models in which the dependent variable(s) enter(s)
nonlinearly. Since the model cannot be solved automatically,
no Actual/Fitted plots, forecasts or simulations are available
in this case. This option is also used for the formulation of
equilibrium relations for ECM models.
"Nonlinear Component"
This is a nonlinear function of regressors, f2, augmenting or
replacing the "Type 2" regressor selection. This component plays a
different role in the model from the f1 specification when there are
autoregressive or fractionally integrated components. Otherwise, f1
(equation) and f2 are effectively equivalent. However, since the
dependent variable(s) are not specified here do not include the "="
in this case.
"Nonlinear ECM"
In error correction models, equations can contain nonlinear
functions f3(Z) of the lagged equilibrium relation Z. Three popular
forms are pre-programmed. For other cases, enter the
function(s) f4 in implicit form, using the reserved variable name
Z# to denote the equilibrium relation or, in case of two or more
relations, the names Z#1, Z#2, ...
Lags can be included as Z#{-j} for j>0. Note that the lag j is
relative to the minimum lag specified in the Model / Equilibrium
Relations dialog. Presample lags are replaced by 0.
"Nonlinear MA"
With this option, the model disturbance term Ut is replaced by
the moving average formulation
Ut = Et - f4(Et-j, j > 0).
Enter the formula for the function f4(.) using the reserved variable
names E#{-j} to represent the disturbances lagged j periods.
(E here corresponds to v in equation (4.29) of the main document.)
As in "Residual" the formula should be in implicit form, do not
include "=".
In multi-equation models, use the variable names E#1{-j},
E#2{-j}, ..., to represent the disturbances for each equation.
Presample lags are replaced by 0.
97
Note:
1.
With this option the function has to be evaluated recursively.
Iterative estimation of these models could be timeconsuming!
2.
A pre-programmed nonlinear MA model can be accessed
from the Model / Dynamic Equation dialog, and should be
faster to estimate than the coded version. Use this option
except to implement other variants. If both options are
selected, the coded version takes priority.
Notes:
1.
For the Equation option, an equation code must pair with a selected
dependent variable - see the field heading. It is not possible to add
an equation without first selecting a variable. Equations can be validly
entered in the explicit format "Dependent Variable = [Formula]".
The name of the dependent variable is added implicitly, if omitted.
2.
In the Residuals option, the dependent variables must still be selected
even though there is no explicit normalization. The number of
equations formulated must be equal the number of selected variables.
Checking that the formulated equations have a solution for the chosen
variables is the responsibility of the user.
3.
For the Residuals option, the typed equations define the model
to be estimated. Dependent variable selections in Model / Dynamic
Equation are ignored! Be sure to delete any unwanted equations
using "Clear".
4.
When "System" is checked in Models / Dynamic Equation, and two
or more endogenous variables are selected, coded specifications can
be created for each equation. Switch between these with the "Next"
and "Previous" buttons. If no function is specified for a variable,
enter "= 0" in the corresponding field.
5.
While linear simultaneous equations systems can feature coded
components (set the matrix B in equation (5.1) of the main
document) simultaneity in coded equations is not allowed for
estimation. That is:
*
"Equation" specifications should contain only exogenous
or lagged endogenous variables on the right-hand side.
*
"Residual" specifications may be estimated, subject to the
caveat of containing only one endogenous variable each.
It is the user's responsibility to respect these restrictions. The
program cannot monitor violations, and incorrect estimates and
simulations will result!!
Note, nonlinear simultaneous equations can be simulated using
the W#1, W#2,... reserved names to denote shocks, see User
Interface / Entering Formulae.
6.
When the "Coded Equilibrium Relations" option is selected in the
Model / Equilibrium Relations dialog, only the Residuals option is
98
selectable in this dialog.
TEXT BOX CONTROLS
"Cancel"
Discard changes and restore existing formula.
"Clear"
Clears displayed formula. Enters left-hand side for "Equation"
entry.
"Next"
Displays the next formula, where present, disabled otherwise.
"Previous"
Displays previous formula where present, disabled otherwise.
"Test"
Tests parsing of the current model equation(s).
Closing the dialog with the Windows Close button [x] is equivalent to
pressing "Cancel".
PARSING THE MODEL
Parsing fails in cases including the following:
*
Variable name does not match any variable in the data set.
*
Non-matching or misplaced brackets/parentheses/braces.
*
Missing/misplaced operators.
*
Wrong left-hand side variable ("Equation").
An error message is displayed in a pop-up window, and should assist the
debugging process
Note: A name not appearing in either the variable list or current parameter
list is assumed to be a new parameter, and added to the list. Check the
list carefully to see if it's what you intend.
PARAMETER NAMES
*
"P[i]" where "i" is the parameter number shown beside the text field, is
always a legitimate choice of name. It must be still typed explicitly in the
field, so that the program knows how many parameters are specified.
*
Nine parameter name fields are displayed by default. To change the
number, type the value in the "Maximum Parameters" field. To redraw
the dialog box click any button, e.g. "Cancel".
*
Be careful that parameter names do not duplicate variable names. The
convention of naming a coefficient by the variable it multiplies must be
avoided here!
*
In multi-equation models, the same names appear in each equation, but refer
to different parameters. They are distinguished in the output by prefixes
"Eq1:", "Eq2:" etc.
*
If a parameter is named but does not appear in an equation, it is fixed at
0 in that equation. It appears in the Values dialog, but is suppressed in the
output. This allows equation-specific parameters to be named distinctively
VARIABLE NAMES
*
These can be spelled out in full or replaced by the short form "x[i]" where
"i" is the position of the variable in the list, starting from 0. The line numbers
are displayed in the variable list in Models / Dynamic Equation whenever
the text field is open.
99
*
Under the "Equation" coding option, select the dependent variable(s)
in the Model / Dynamic Equation dialog first. Unless the formula fields
already contain formulae (press Clear to delete these), opening a field
will automatically insert the variable name and " = ", ready for the rest
of the formula to be typed.
SIMULATING CODED EQUATIONS
Any coded functions of "Equation" type can be simulated. Normally, the
generated disturbance is added to the coded function to simulate the dependent
variable. However, a special feature available for simulation models is to include
the disturbance as a coded component, which can therefore be transformed or
enter the model nonlinearly.
*
After selecting "Equation" in this dialog, represent the disturbance by the
reserved name W#, or W#{-j} for lagged values. See 1.5 General /
Entering Formulae for further details. If the reserved name W# appears in
one or more equations of a model, shocks are not added to any coded
function(s). Therefore, in a multi-equation model, every equation must
have its shock included explicitly in the formula if any one equation does.
*
Models with these features cannot be estimated. If the W# reserved name
appears in an equation for estimation, an error message is generated.
However, it will often be possible to estimate the same model in a different
formulation. Code the function separately for estimation, by selecting
"Residual" in this dialog and creating the counterpart nonlinear equation
for W#. The reserved names E#{-j} can be used to represent the lagged
residuals, in this context.
*
In equation systems, the generated shocks are written W#1, W#2, etc.
It is possible to simulate models having a recursive (triangular) structure.
The equations are solved sequentially, and equations numbered 2 or above
can contain solutions from the preceding equations. These are coded using
the reserved names E#1, E#2, etc.
NOTE: Such equations cannot be estimated, in general! TSM can handle
only linear simultaneity in estimation.
SIMULATING WITH RANDOM EXPLANATORY VARIABLES
Monte Carlo experiments may need to be conducted under "random regressor"
assumptions, so that the estimators simulated are marginalized with respect to
the distributions of exogenous variables. One way to achieve this is to set up a
recursive (triangular) multi-equation model, in which one or more equations
generate the explanatory variables. Another way is to insert normally
distributed random numbers directly into the relevant columns of the data matrix
prior to the simulation. This method is generally more numerically efficient, and
is particularly useful in models such as the probit, logit, Poisson etc. where only
single-equation estimation is currently supported,
*
To enable this feature, simply reference a variable in the coded equation
as X#[i] where i represents the column number of the data matrix.
(Referring to the variable by name is not supported.)
100
*
Only standard normal data can be generated in this way, but the equation
coding might apply transformations to yield modified distributions.
*
Don't forget that the previous contents of the data set are over-written
each time a simulation is run. It's recommended to create "placeholder"
variables to hold the generated data. Do this using the "Make Zeros"
and "Rename" commands in the Setup / Data Transformation and
Editing dialog.
OX CODING
See Appendix C of the main document for information on compiling supplied
code into the program.
Supplied Ox code can be used to return five types of object, according to the
selection made with the radio buttons Residuals: Return a vector/matrix of equation residuals, as a function of
data and parameters from UserEquation(). Return solved
values and forecasts from UserSolve().
Log-likelihood:
Return a vector of log-likelihood contributions as a function of
data and parameters from UserLikelihood().
Statistic:
Return a statistic or vector of statistics as a function of data
and optional constants (passed as parameters) from
UserStatistic().
Data Generation:
Return a generated data set as a function of existing data and
constants passed as parameters from UserGenerate().
Test Only:
Choose this setting if the only coded function to be returned is
a test statistic from UserTest(), based on the regular estimation
outputs, selected with the "Test" checkbox. If this option is set,
the "Coded Function" checkbox is automatically deselected.
Notes.
1.
If the coded functions have been set up for selection by name, as described
in Appendix C, they can be selected in the dialog using the Previous and
Next buttons to navigate the list. Preset names cannot be edited. If no naming
function has been defined, a function can still be selected by typing its name
into the field.
1.
The test statistic option, from UserTest(), accessed by checking the "Test"
checkbox, is compatible with any estimated model. This includes linear
equations, and the Ox Residuals and Log-likelihood options, but not Statistic
or Data Generation.
2.
If a coded test is the only programmed option, select "Test Only" and
do NOT check the "Coded Function" checkbox in Model / Dynamic
Equation.
101
3.
If "Coded Equilibrium Relations" is selected in Model / Equilibrium
Relations, and "Equilibrium Relations" is checked in Model / Dynamic
Equation, the "Coded Function" checkbox in in Model / Dynamic
Equation is disabled. Note that in this case the parameter values for the
coded relations are displayed in Values / Equilibrium Relations
4.
For all options except the coded test and coded equilibrium relations,
the "Coded Functions" checkbox must be checked in Model / Dynamic
Equation to activate the option.
5.
Enter names of parameters in the text fields provided in the dialog.
Optionally, an identifying name can be entered in the 'Function Name'
field. This is used to identify the output and can also select the function
from a code library maintained in the run file. Alternatively, a name
can be passed from the function itself. To activate this option, leave the
Function Name field blank.
6.
When residuals or the log-likelihood are returned, setting dependent
variable(s) in the Model / Dynamic Equation dialog is optional, though
recommended. If set, it/they should correspond to the normalized
variable(s) in the supplied functions. These settings are not used to
compute the estimates, but allow the correct plots, series and
forecasts to be generated.
7.
It is the user's responsibility to set the sample period (see Setup / Set
Sample) to ensure that all observations are available for the variables in
the model. This is done automatically for models specified through the
program options, but the program cannot know whether variables
included in the user's function have missing observations.
8.
For statistics and data generation, there is the option to enter names
for constants in the parameter name fields, then set values for these in the
Values / Equation dialog. These values are not modified by TSM, but
are passed through directly to the user's function. If this feature is utilised,
it provides a means for quick changes of specification, without editing the
code.
9.
To generate data, "placeholder" variables must exist in the data set. The
contents of these columns is unimportant, being replaced by the generated
series when the simulation runs. For example, they can be created using the
Extend Sample, Make Zero and Rename commands in Setup / Data
Transformation and Editing. Then select these variables as the Dependent
Variable(s) in Model / Dynamic Equation.
4.7 Model / Regime Switching...
This dialog allows the choice of
*
number of regimes,
*
type of switching - simple Markov switching, explained switching, Hamilton's
model, or smooth transition (ST).
*
which model components to switch,
102
*
specification of the explained switching probabilities or transition function,
where these options are selected.
Notes:
1.
Regime switching is not activated until at least one model component is
selected for switching!
2.
Except for the smooth transition model, regime switching requires a timedomain maximum likelihood estimator. Options are "greyed out" until
a valid selection is made.
3.
The option "Estimate Regime Differences" selects the parameterization that
allows individual significance tests of differences between the regimes.
However, note that in a test for *no* differences between regimes (= test
for number of regimes) the switching probabilities or ST parameters are
unidentified under the null hypothesis. This is a well-known testing pitfall,
and the standard tests don't apply.
MARKOV SWITCHING
4.
If "Estimate Regime Differences" is selected with Markov or Hamilton
switching, then rows 2,...,M of the Markov transition matrix are likewise
expressed as differences from row 1. This allows a test of the hypothesis
that transition probabilities are independent of the current regime.
5.
In the Markov and Hamilton models, both the matrix of estimated transition
probabilities p_{ji}, and the unrestricted parameters t_{ji} with standard
errors are reported in the output. The latter are labeled "Logistic of P(j|i)".
See the main document for details.
6.
In Hamilton's model, the "Intercept" selection in Models / Dynamic
Equation is ignored. The intercept is specified as shown in the TSM
document.
7.
Analytic forecasts are available for the Markov switching models.
However, the number of calculations needed to compute the multi-step
forecast 2-standard error bands increases exponentially with the number
of steps, and can become excessive. Standard error calculations are
terminated after 100 seconds has elapsed, and only the point forecasts
are reported for further steps. A warning message is printed in this case.
The SE bands can also be omitted, see Options / Graphics.
EXPLAINED SWITCHING
8.
In the explained switching case, the radio buttons allow the choice of
variables to explain the probability of switching into the given regime at
date t. An intercept can be optionally added to the equation.
9.
Distributed lags are not implemented for explained switching and smooth
transition models, but the 'Lag' scrollbar allows a fixed lag to be applied
to the variable(s). If and only if the lag is positive, the dependent variable(s)
can be included in the set.
103
10.
There are two versions of the explained switching model. In the first
version, the equation for the probability of switching into regime j at date t
may depend on the current regime (i) only through an intercept shift, by
inclusion of a dummy variable for the intercept in question, with Regime 1
as the reference case. In the second version, the switching equations may
be fully regime-dependent, and switch just like other model components.
Check the box "Regime-Dependent Coeffs." to enable this case.
11.
The second explained-switching model contains the first one as a special
case, but the latter is set up in a slightly different way, with regime dummies,
and is retained for backwards compatibility and simplicity. If dummies (or
switching intercepts) but no explanatory variables are specified in explained
switching, the model represents an alternative parameterization of the regular
Markov-switching model.
SMOOTH TRANSITION
12.
In the smooth transition (ST) case, select the transition indicator (z_t) from
the variable list after clicking the first radio button. Only one selection is
possible. If no transition indicator is selected, the smooth transition option
is cancelled and the type setting reverts to Markov switching.
13.
The inclusion of an ST intercept is selected by a checkbox. If both this and
explanatory variables are omitted, the dominant regime depends on the sign
of z_t. The second set of parameters is unavailable unless 'Double
Transition' is checked.
14.
The number of regimes is fixed at 2 for the ST model.
15.
NOTE: The explanatory variable selections for the explained switching and
smooth transition options share a common storage location. If the type of
switching selected is changed, the existing variable selections for these
options are cancelled.
16.
Analytic forecasts are not available for ST models in this release. Use the
Monte Carlo forecast option.
17.
The ST model has two identical maxima of the likelihood, since
interchanging both the regimes and the sign of the smoothness parameter
(gamma) yields the same likelihood, by construction. Be careful to
interpret the estimates correctly.
4.8 Model / Equilibrium Relations...
An Equilibrium Relation (Eq.R.) is defined as a linear combination of lagged
variables that is inserted as a "regressor" in one or more equations of a system,
with the combining coefficients being either restricted or estimated. This is
sometimes called an Error Correction Model (ECM). Most often, an Eq.R. has the
interpretation of a cointegrating relation in a system of I(1) variables, although it
could also, in principle, appear in a model of stationary processes. Eq. R.s can
also appear in single equations, in which case they implement a re-parameterization
of the dynamic model in "ECM" form.
104
*
Choose one of the three options for specifying the equilibrium relation(s).
A:
Select "Linear Equilibrium Relations" to specify the relation(s)
by choosing variables from the list.
B:
Select "Nonlinear AR / Closed VECM", to include the set of
dependent variables as lagged regressors automatically.
C:
Select "Coded Equilibrium Relations" to specify nonlinear
equilibrium relations using the Coded Function dialog.
*
Use the first scroll bar to select the number of Eq.R.s to be included in the
model.
*
Use the second scroll bar to chose the lag to apply to the Eq. R.s
(must be >0).
*
Restrictions on each relation are set up in the Values \ Equilibrium
Relations dialog.
Notes:
Options A and B
1.
Every Eq.R. must contain at least one fixed coefficient, otherwise the
relation will be unidentified. Set the fix in the Values / Equilibrium
Relations dialog. If no restriction is set manually, the first coefficient in
the list will automatically have its coefficient set to 1 when the
estimation is run.
Note: The Values button is highlighted if two or more coefficients are
restricted in any relation.
2.
With two or more Eq.Rs, note that this dialog specifies the variables to
appear in all of them. To create distinct relations, exclusion restrictions
(fixing coefficients at 0) must be set up in Values / Equilibrium Relations.
Note: For consistent estimation, the relations should satisfy the standard
rank conditions for identification of a linear system.
3.
When "Closed VECM" is checked, the lagged variables included in the
VECM are the dependent variables LESS the fitted combination of Type
1 intercept and/or Type 1 regressors. See main TSM document for
details of the specification.
Option C
4.
The equilibrium relations are formulated as the function f5 in the Model /
Coded Function dialog. Note that "Residual" format must be used (no "="
in the field). This is the only permitted option when option C is selected
in this dialog.
5.
When "Coded Equilibrium Relations" is checked, and "Equilibrium
Relations" is also checked in the Model / Dynamic Equation dialog, the
"Coded Function" checkbox is disabled - coded functions can appear
either in the main equation(s) or in equilibrium relation(s), but not both
at once.
105
6.
The number of relations in the model is determined by the number
specified in the Model / Coded Function dialog. This overrides the
setting in this dialog.
7.
Formulating the relations with enough restrictions to ensure identification
is entirely the responsibility of the user. Use this option only if you know
what you are doing!
8.
The specification of the relations can be different when there are two
or more of them. They nominally contain the same parameters, but these
can be automatically fixed at 0 if not included in a particular relation.
See Model / Coded Functions for details. They can also be restricted in
the The Values / Equilibrium Relations dialog, if desired.
All Options
9.
Eq.R.s are only included in the model if this feature is selected in Model /
Dynamic Equation.
10.
The radio buttons in the "Types of ECM" area allow selection of nonlinear
response mechanisms as well as the usual Linear case. See the main
document for details. Three popular variants are pre-coded. Use the
Model / Coded Function dialog to define other cases.
11.
Check the first checkbox in the "Fractional Cointegration" area to implement
a fractional cointegration (F-VECM) model. Note that this option is ignored
unless the VARFIMA / Fractional VECM box is checked in the Dynamic
Equation System dialog. In this case, setting the "Impose Unit Root" option
causes the estimated value(s) of d1 to be smaller by 1 than otherwise.
This is taken into account in the calculation of the cointegration order(s) d3,
such that the equilibrium relations appear differenced to order 1+d1-d3 in
the system.
12.
Check the second checkbox to select the generalized cointegration model.
In this case, the cointegrating variables may be fractional differences of the
measured variables. See the main document for details.
13.
The checkbox labelled "Diffs Spec'n for FI & ECM Pars" controls the option
of estimating certain parameters in equations 2,..., N as the differences from
the corresponding parameters in Equation 1. The parameters in question are
the fractional integration parameters d1 and d3, and the parameters of the
nonlinear ECM adjustment mechanisms. The option allows the restriction
of equal parameters to be both tested and imposed, in the latter case by
putting the parameters for equations 2,...,N to zero and setting the "Fixed"
checkboxes, in the values dialog.
NOTE: It is not necessary to specify a fractional VECM to set this option.
It applies also to a regularly-cointegrating or non-cointegrating VARFIMA
model, and also to the fractional lag parameters of a system FIGARCH
or HYGARCH specification.
14.
If "Impose Unit Root" is specified in Model / Dynamic Equation, the
VECM is estimated with unit roots imposed in the short-run dynamics,
106
while the Eq. R.s enter as lagged levels.
4.9 Model / Parameter Constraints...
This dialog sets options for imposing restrictions on the coefficients.
Three types of restrictions can be set up:
a)
zero restrictions,
b)
multiple linear restrictions, and
c)
general restrictions specified as coded formulae.
In case (b), only the constants (intercepts) of the constraint functions
are set in this dialog. The linear functions themselves, like the parameters
for zeroing, are set in the Values dialogs.
Restrictions can be implemented in either of two ways:
*
Tested on the unconstrained estimates, using the Wald principle,
*
Imposed in estimation.
In the latter case, the LM test for the restrictions is computed, if this option is
selected in the Options / Tests and Diagnostics dialog. In this case, any fixing
restrictions on the parameters will be treated as part of the maintained model
and not tested. To test fixing restrictions, make sure the Parameter Constraints
option is deselected in Model / Dynamic Equation... or Model / Linear
Regression
Notes:
1.
Up to 10 linear restrictions can be specified with nonzero constant terms.
However, up to 20 additional restrictions could be set with zero constant
terms.
2.
Estimation subject to constraints is not available with OLS and IV estimation.
This option is disabled ("grayed out") when the Model / Linear Regression
dialog is open.
3.
By default, the statistic reported is asymptotically chi squared. Set the
check box to report the F statistic, with the reported p-value taken from
the F tabulation. Note that this setting is shared with the user-specified LM
and moment tests (see Actions / Compute Test Statistics). It can be
selected/deselected in any of the relevant dialogs.
REGRESSOR SIGNIFICANCE TEST
4.
The option "Test Joint Significance of Regressors" provides a valid time
series implementation to the "F test of the regression" computed by many
packages.
5.
In a single equation it sets up a Wald test of the joint significance of all
regressors in the mean model, all Types and components of equilibrium
relations (if any) but excluding the intercept, trend and seasonal dummies,
and lagged endogenous variables. The null hypothesis can therefore be set
up as a univariate time series representation of the dependent variable.
107
Note that this test can be performed in the usual way by selecting the
parameters individually in the Values dialogs, but this option provides a
handy shortcut.
6.
The program "knows" a regressor is a seasonal dummy if the string
"seasonal dummy" or "seasonal dummies" is part of the data description.
This is set up automatically if the dummies are generated in Setup / Data
Transformations and Editing.
7.
In equation systems, all exogenous regressors of all types in all equations
and in equilibrium relations are included in the test, but intercepts, trends
and current and/or lagged endogenous variables are excluded.
"Endogenous" means any variable explained by the system.
8.
Additional parameters can be added to the test set in the usual way, by
checking the relevant "Wald Test" box in the Values dialogs.
9.
Variables having parameters "fixed" are excluded from the test.
CODED_RESTRICTIONS
10.
A coded restriction on the parameters is set up by typing the equation
into a text field. After selecting the restriction type with the radio button,
press the Code button to open the text box.
TEXT BOX CONTROLS
"Cancel"
Close box, discarding changes.
"Delete"
Delete the currently displayed formula.
"Next"
Displays the next formula, where present.
"New"
Opens a new blank formula where there is no "Next".
"Previous"
Displays previous formula, where present.
"OK"
Closes the text box and stores current formulae.
[Return]
Equivalent to pressing "OK".
Closing the dialog with the Windows Close button [x] is equivalent to
"Cancel".
For information on entering formulae, see Section 1.5
11.
Parameters can be written in the notation "a[i]" where "i" is the number
appearing in the left-hand column in the Values dialogs. "p[i]", "A[i]"
and "P[i]" are all permitted variants, but the square brackets are
mandatory, note.
CAUTION: Parameters can also be identified by name. However,
some parameters are named differently in the Values dialogs and in
the output. If in doubt use the number notation, which is unambiguous.
12.
Suppose there are P restrictions. Using the numbering notation
described in Section 1.5 (in practice, parameter names can also be
used) the restrictions must be entered in the solved form
a[j1] = f1(a[k1],...,a[kM])
...
a[jP] = fP(a[k1],...,a[kM])
for k1,...,kM not equal to j1,...jP, where f1(),..,fP() are differentiable
algebraic expressions. The program imposes the restrictions by
108
replacing a[j1],...,a[jP] with the given functions of a[k1],...,a[kM].
13.
Restrictions cannot be entered in implicit form!
Example:
a[0] = a[1]*a[3];
a[2] = exp(a[1] - a[4]);
is OK.
a[0] = a[1]*a[2];
a[2] = a[1] + a[3];
is NOT valid! (Not solved form.) A valid form of the first
equation would be
a[0] = a[1]*(a[1]+a[3]);
4.10 Model / Select Instruments...
This dialog is enabled only if IV/GMM is the selected estimator.
*
Highlight by clicking with the mouse those variables to be included as
instruments.
*
Use the checkboxes to indicate whether the intercept and trend dummies
are to be included as instruments.
*
Use the "Additional Instruments" scrollbar to set the number of lags of
additional instruments to be used.
*
Use the "Lagged Endogenous" scrollbar to set the number of lags of
endogenous variables to be used as instruments.
*
The Clear button unselects all variables in the list.
Notes:
1.
Any non-lagged variable appearing in the equation but not appearing in the
instrument list is treated as endogenous.
2.
Any variable appearing in the instrument list but not in the equation is an
additional instrument. Set the first scroll bar to select the number of lags of
these variables to include in the instrument set.
3.
To use lagged endogenous variables as instruments, set the second scrollbar
to the number of lags to be included:
o
If this scrollbar setting is zero, no lagged endogenous variables are
used as instruments.
o
If this scrollbar setting is positive, the number of lags of a variable
included as instruments is the greater of this setting and the number
of lags specified to appear in the equation, according to the lag
setting of the variable's Type.
4.
The normalized (left-hand side) variable (or variables, in a system) cannot be
selected in this dialog, since they are necessarily endogenous. Its (their) lags
109
are included automatically if the second scrollbar is set to a positive value.
5.
Lags can be be created manually for use as instruments in the Setup / Data
Transformation and Editing dialog. However, be careful with the automatic
lag settings in this case. If lags are double-counted, the instrument matrix
will be singular!
6.
In panel data models the intercept is suppressed under certain data
transformations such as individual mean deviations and first differences.
When these options are selected the instruments are subjected to the
same transformation. The intercept is not available as an instruments in
these cases, and the checkbox is disabled.
110
5. Values
5.0 Values: General
The Values dialogs are used to operate on model parameters. They allow
*
setting starting values for the search algorithm.
*
fixing parameters at chosen values in the estimation.
*
setting bounds on parameters, for estimation subject to inequality constraints.
*
setting a range for a grid evaluation of the estimation criterion, in one or two
dimensions.
*
selecting parameters for Wald significance tests.
*
setting up linear functions of parameters for Wald restrictions tests.
Unlike the other dialogs having fixed layout, Values dialogs can be resized.
Grab the border and drag with the mouse.
BUTTONS
1.
The "Refresh" button rewrites the values field to reflect changes to the model
specification. Pressing the "Values" button in the relevant Model dialog has
the same effect.
2.
Press the "Clear" button once to set all free values to defaults. Fixed values are
left unchanged. Press the button a second time to clear all settings, including
parameter fixes. Pressing the Refresh button resets the function of the Clear
button.
3.
In the Equation and Equilibrium Relation dialogs, when more than one
equation/relation is specified, [>] and [<] buttons are displayed on the button
bar. Use these buttons to cycle through the equations/relations, respectively
forwards and backwards.
4.
All dialogs except Markov Probabilities and Smooth Transition have
"Regime:" [>] and [<] buttons that appear when switching regimes are
specified. Note that if the parameters in question have not been selected to
switch, then Regime 1 shows the common values for all regimes.
The dialogs for Regime 2 and above are then blank.
5.
An alternative navigation method is to use the choice widget(s) on the tool
bar. First choose the equation/relation/regime values to be displayed.
Change the display by either double-clicking the widget, or pressing the
"Refresh" button in the Values dialog.
6.
All dialogs have a checkbox for selecting the parameter bounds and grid
plotting layout. This control is located at the bottom of the panel, it may be
necessary to scroll the display view it. It shows/hides two columns of text
fields for entering bound values - see paras 11-15 below. Checking/
unchecking the box in any dialog effects the setting in all the Values dialogs.
111
VALUES FIELDS
7.
The values attained in an estimation run are displayed in the Values fields to
double-precision machine accuracy. These provide the starting values for a
new run, and can be edited.
FIXED PARAMETERS
8.
Check 'Fixed' to fix the parameter at the value set, during estimation.
Applications of this feature include:
*
Suppressing intermediate lags in ARMA/GARCH models (fix the
values at zero).
*
Temporarily restricting a model, without changing the specifications.
*
Computing LM tests of the corresponding restriction(s) - see
Options / Test and Diagnostics Options.
*
Evaluating the optimized likelihood over a grid of points - see paras.
13-14 below and also Actions / Plot Criterion Grid for more details.
9.
If the model specification is changed, values are reset to defaults. To remove
a variable or lag from the model temporarily, "fix" its parameter at zero.
This preserves other stored values.
10.
As a reminder that one or more parameters are fixed, the Values buttons in
the corresponding dialogs are highlighted, and check-marks appear against
the Values menu items.
PARAMETER BOUNDS
11.
To constrain a parameter to lie in an interval, enter the upper and lower
bounds in Values but do not check the 'Fixed' box. The reported parameter
is then a logistic transformation of an underlying, unconstrained value.
The bounds are ignored unless the upper strictly exceeds the lower.
Cancel the setting by putting both bounds to 0.
12.
If the estimate is in the interior of the interval, the standard error is
approximated using the delta method. However, if the constraint binds in
the sample, the covariance matrix may be near singular and standard
errors unavailable or unreliable. It may be best to re-estimate with the
parameter fixed at its boundary value, in this case.
13
It is not recommended to use this technique routinely to impose, e.g.,
positivity and stability constraints on lag polynomials. The search
algorithm should usually work OK without this. The method is implemented
more as a last resort for difficult cases.
GRID PLOTS
14.
If bounds are set and the 'Fixed' box is also checked, the bounds will be
used as the limits of a Grid Plot. Either one or two parameters can enter the
grid. If the 'Fixed' box is checked and both bounds are 0, then the parameter
in question is simply held fixed when the grid is drawn. If three or more
parameter are both fixed and have bounds set, the first two encountered are
the plotted parameters. The others are just treated as fixed in the usual way.
112
15.
The number of grid points must be set in the Options / Optimization and Run
dialog. The number is counted from zero. Thus, if the bounds are 0 and 1
and it is desired to evaluate at intervals of width 0.1, enter 10 in this text field.
The likelihood will then be evaluated at 11 points, 0, 0.1,0.2,…,1.
WALD TESTS AND LINEAR RESTRICTIONS
16.
To compute a Wald test of joint significance, enable "Wald Tests" in the
Model / Linear Regression dialog, or "Parameter Constraints" in the Model
/ Dynamic Equation dialog. Then check the checkboxes of the variables to
be included in the test.
17.
If the option to test joint significance of the regressors is selected, these are
included automatically, and do not need to be checked her. Any additional
parameters checked here will be added to the test set.
18.
To compute a Wald test of linear restrictions Rb = c, or impose these
restrictions in estimation, the number of restrictions and the elements of c
must first be entered in the Model \ Constraints dialog. Then, refresh the
Values dialog and enter the columns of R' (i.e., the rows of R, transposed)
in the fields displayed.
19.
A restriction can involve any subset of model parameters, and hence can be
spread over two or more number of Values dialogs. It may be helpful to open
the relevant dialogs together and arrange them on the screen in a column.
Restrictions may also be applied across equations and across regimes. Since
only one equation/regime Values dialog can be displayed at a time, use the
choice widgets or "Next..." buttons to switch quickly between them.
20.
For each linear restriction, one parameter must be designated to be "solved"
as a function of the remainder. Make this choice by checking the relevant
"Constrained"/"Wald test" checkbox. There must be same number of checks
in this column as restrictions, otherwise an error message is generated.
It is also the user's responsibility to be sure that the restrictions can be
solved uniquely for the checked parameters - in other words, the square
sub-matrix of R' defined by the checked rows must be nonsingular. If this
property does not hold, an error message is generated.
5.1 Values / Equation...
This dialog sets the parameters specified for an equation, including specifications
set in either the Linear Equation dialog or the Dynamic Equation / Conditional
Variance / Supplied Function dialogs.
Notes:
1.
The Parameter Bounds / Grid Plotting checkbox affects all the Values
dialogs. When checked, a text field is displayed to set the number of
grid points for criterion plotting.
2.
In multi-equation models, use the "Equation:" [>] and [<] buttons to
cycle through the equations, either forwards or backwards. Alternatively,
113
select an equation using the "Equation" choice widget on the tool bar and
and then press the "Refresh" button. In regime-switching models, to see
the different regimes use the "Regime:" [<] and [>] buttons, or the
"Regime" choice widget, similarly.
3.
If a BEKK multivariate GARCH model is specified, the ith columns
of the matrices A_j and B_j are displayed in the dialog for equation i,
as Alphaj(i,k) and Betaj(i,k), for k = 1,...,[number of equations].
Be careful to note how these matrices enter the model - see the main
document for details. Although entered and reported in the same
style, these matrices are not comparable with the multivariate GARCH
specification. Be careful to interpret them correctly.
4.
DCC dynamic parameters are displayed in the Values / Distribution
dialog.
5.2 Values / Equilibrium Relations...
This dialog shows parameters of the equilibrium relation(s).
Note:
1.
If more than one relation is specified, use either the [>] and [<] buttons
in the dialog, or the "Equation" choice widget on the tool bar, to switch
between them.
2.
At least one of the parameters in this dialog must be fixed at a non-zero
value (the normalized variable). If none is specified manually, the first entry
is automatically fixed at 1 when the equation is run.
5.3 Values / Distribution...
This dialog shows parameters defining the distribution that are not associated
with any one equation in a multi-equation model. These are:
*
the Student t parameters (degrees of freedom and skewness)
*
parameter of the GED distribution
*
parameter of the negative binomial distributions
*
error correlations.
*
Parameters of the DCC multivariate GARCH model
Notes:
1.
In regime-switching models, use the [>] and [<] buttons to cycle through
the regimes, or the "Regimes" choice widget on the tool bar, with
"Refresh", to select a regime directly.
2.
Covariance parameters of the BEKK multivariate GARCH model,
while not associated with any one equation, are nonetheless displayed in
the Values \ Conditional Variance dialog. See Help page 5.2 for
correct interpretation of these parameters.
5.4 Values / Switching Regimes...
This dialog displays parameters specified in the Model / Regime Switching dialog.
114
*
In the Markov switching case (including Hamilton's model) these are
the transition probabilities p_{ji} = P(j|i), forming a M´(M-1) matrix.
These are the probabilities of switching from regime i to regime j.
*
In the Explained Switching and Smooth Transition models, the dialog shows
the parameters of these switching models.
Notes:
1.
In the Markov case, the switching probabilities are constrained to be positive
with their sum in [0,1], such that the implicitly defined Mth probabilities are
nonnegative. These are transformed to unconstrained values t_{ji}for
estimation using a logistic map. See the main document for the mapping
formulae. These values are displayed in the output, with standard errors.
2.
To show the t_{ji}values in the dialog, with upper and lower bounds
transformed similarly when shown, check the "Display Logistic
Transformations" checkbox.
3.
By selecting the "Estimate Regime Differences" option, the Markov
switching probabilities can (for example) be constrained not to depend on the
current state. Under this hypothesis, the sample is simply a random mixture of
regimes prevailing with the unconditional switch probabilities. Note that the
null values of the "incremental probabilities" of regimes 2,...,M are 1/M,
corresponding to t_{j2} = ... = t_{jM} = 0.
4.
If regime-dependent coefficients are specified in Explained Switching, use the
"Next Regime" button to cycle through the regimes, or the "Regime" choice
widget on the toolbar to select a regime directly.
5.
Note that specifying only the intercept and regime dummies in the explained
switching model provides another way to estimate the simple Markov
switching model, in an alternative parameterization.
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6. Actions
6.1 Actions / Run Estimation
Closes all dialogs, saves the current configuration in "settings.tsm", and starts
estimation of the currently specified model.
To have the dialog box configuration restored automatically after the run is finished,
select this option in General Options. Alternatively, re-open by hand with Actions
/ Restore Dialogs.
Notes:
1.
This command can also be started with the "Run" button on the toolbar, and
with the "Go" buttons in the Model / Linear Regression and Model /
Dynamic Equation dialogs.
2.
Sequential and iterative calculations can be interrupted while in progress, by
clicking the "Run" button on the toolbar. A choice box appears, possibly
after a short delay, with the option of aborting the run, or continuing.
BATCH JOBS
3.
If the checkbox "Run Next Estimation as External Process" is checked
in Options / Optimization and Run before the command is given, the run is
performed externally by starting a new instance of Ox.
4.
If the checkbox "Defer External Jobs" is checked in Options / General, the
Ox file containing the job is created, but not run. Use this option if the
job is to be run on a different machine, for example.
6.2 Actions / Evaluate at Current Values
This command is the same as Actions / Run Estimation except that the
optimization algorithm is not called. The post-estimation output is simply created
at the parameter values currently stored in the Values fields. Note that these are
the estimates, following an estimation run. This option can be used, for example,
to obtain test statistics, forecasts, listings etc. for a model that has just been
estimated, without repeating the optimization.
Notes:
1.
This command is also launched by the "Evaluate" button on the toolbar.
2.
If Linear Regression or Cointegration Analysis dialogs are open, the
command has the same effect as the 'Go' buttons and Actions / Run
Estimation.
6.3 Actions / Estimate Multiple ARMA Models
Estimates a sequence of models with increasing ARMA orders, starting with
ARMA(0,0). All other features of the model are as currently specified,
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although regime switching options are disabled. The limits of the sequence are
set in the Setup/Multiple ARMA Models dialog.
Notes:
1.
Starting values are set to either the estimates from the preceding
specification, or zero, as appropriate. The ARFIMA(0,d,0) is initialized
with Robinson's (1994) nonparametric estimator of d.
2.
Other selected model features (regressors, conditional heteroscedasticity,
supplied function) are estimated as usual, with the supplied starting values,
for each case.
3.
Post-estimation options (forecasts, correlograms, graphics, impulse
responses, tests, series output and retrieval) are suspended. Re-estimate
the selected model to get these outputs.
4.
This option cannot be used in conjunction with regime switching, nor
with multiple-equation models.
5.
The model optimizing each of the selection criteria (Schwarz, Hannan-Quinn
and Akaike) is reported following the run.
6.4 Actions / Automatic Regressor Selection
Given a baseline model containing N regressors of one or more Types
(including current and lagged values of some variables, typically), this
option estimates all the 2^N possible models formed by taking subsets of
the full regressor set. It then reports the case which optimizes the chosen
selection criterion, which can be either the Akaike (AIC), the Schwarz
(SIC) or the Hannan-Quinn (HQC).
Notes:
1.
Optional settings are selected in Setup / Automatic Model Selection
(regressor Types), which also features an alternate launch button, and
Options / Tests and Diagnostics (selection criterion).
2.
The program excludes regressors from the baseline specification by
turning their "Fixed" flags on, and setting the coefficient values to 0.
In other words, the baseline specification is not actually changed during
the run. To use the selected model for further work, it must be specified
manually in the usual way. If the baseline specification includes regression
parameters that are already "Fixed", this setting is retained and the variable
in question is excluded from the search
3.
The procedure optimizes exhaustively over the model space, looking
at every case, and hence it is path independent and does not depend
on test outcomes. Thus, it is not a "general to specific" search, nor
"specific to general", but in fact both. The limitation is that it cannot
feasibly examine such large model spaces some other automatic
specification search packages that are currently available, which are
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selective in the cases they examine.
4.
The procedure can be used with any model except regime switching,
including equation systems, although it only searches over regressor
choices. Any other model features will correspond to the baseline
specification, and the search is conditional on these. Note that the number
of models needing to be estimated may be very large. For example, with 4
variables and 4 lags (+ current values) N = 20 and the choice is over
2^20 = 1048576 cases. This is feasible for OLS, but probably not for
iterative estimation.
5.
There is no option to print all the estimation results. The output includes
the baseline model, and the optimal case.
6.5 Actions / Recursive/Rolling Estimation
This option estimates the same model for a succession of samples, either of
increasing size with fixed starting point (incremental estimation) or fixed size with
moving starting point (rolling estimation). We call these procedures "recursive
estimation", and while they are not recursive in the strict sense of using an updating
formula to modify the estimator with the extra observation at each step, (it is
computed afresh) the current estimates provide starting values for each new step.
See the Setup / Recursive/Rolling Estimation... dialog for details of setting up the
run.
The sequence of results for each sample period can be exported to a file, according
to the setting in Options / Output and Retrieval Options, or viewed as graphics. The
items available are the parameter estimates with 2-standard error bands, plus
(optionally) regression statistics including criterion values, residual moments,
autocorrelation tests, stability (ex-post forecast) tests, and also any tests of
parameter restrictions that have been set up.
Notes:
1.
The sequential model selection criteria are not recorded. These would differ
from the estimation criterion by the same fixed amount in each run, so the
latter contains all the relevant information.
2
If N-step-ahead ex ante forecasting is specified (see Options / Forecasting
and Simulation) the Nth forecast step and standard error (or percentiles for
Monte Carlo forecasting) are reported in the output. By default, N is fixed
so that the actual date forecast moves forward with the sample. There is an
option to keep the terminal forecast date fixed, so that N contracts as the end
of the sample advances. See Setup / Recursive/Rolling Estimation for details.
3.
This command is launched by the "Run" button on the toolbar if the Setup /
Recursive/Rolling Estimation dialog is open.
4.
On checking the "Report Convergence Status" box, a sequence of symbols
is printed in the results window to show the result of each numerical
118
optimization.
+
denotes strong convergence of the search algorithm
?
denotes weak convergence of the search algorithm
!
denotes failure to converge
(See the Ox documentation for the definitions of these cases.)
This option has no effect in the case of non-iterative estimation.
6.6 Actions / Plot Criterion Grid
Use this option to create a contour plot of the concentrated criterion function.
"Parameter Bounds / Grid Plotting" must be enabled in the Values / Equation
dialog.
The choice of parameters for plotting and the bounds of the grid are set in the
appropriate Values dialog(s). The operation is carried out on the first one, or
two, parameters satisfying the following conditions:
1.
the "fixed" flag is set;
2.
the upper bound exceeds the lower bound.
The criterion function is maximized with respect to all other parameters, holding
the selected one(s) at the grid values. Normal output is suppressed. A progress
bar shows the progress of the calculations.
The number of grid points can be set in a text box in either in Options /
Optimization and Run, or in Values / Equation.
The grid of criterion values can be
* Printed in the results window:
Check "Criterion Grid" in Options /
Output and Retrieval / Print in Results
Window, before running the option.
* Exported to a spreadsheet:
Select File / Listings / Export
Spreadsheet / Criterion Grid after
running the option.
* Plotted on a graph:
Select Graphics / Criterion Plot after
running the option.
Notes:
1.
Other parameters can be either fixed or free for this operation. If a pair
of grid bounds for a fixed parameter are both set to zero, the parameter
is treated as fixed, in the usual way.
2.
A choice of contour plot and surface plot is available for the twodimensional case. Select the option required in Options / Graphics.
3.
Default output to the results window includes the grid location of the
criterion maximum, and locations of the largest values of the test
statistics including absolute t ratios, diagnostic tests and any specified
tests.
4.
Remember that the criterion is optimized (# Grid Points)^2 times
119
in the case of a two dimensional grid. Choice of the number of
points may need to depend on considerations of computing time.
5.
This option can be used to implement tests where parameters are
unidentified under the null hypothesis. The usual procedure is to base
a test on the supremum of the statistic over eligible values of the
unidentified parameter(s)
6.7 Actions / Multi-Stage GMM
This command allows the computation of efficient GMM estimates, where the
weights matrix is estimated to allow for heteroscedastic or autocorrelated errors.
This is a two- or multi-stage procedure, performed by issuing this command
repeatedly. Proceed as follows:
*
Select the covariance formula required ('Robust' or 'HAC' in Options \
Tests and Diagnostics.)
*
Select GMM as the estimator in Setup / Estimators and Sample.
*
Formulate the equation(s) in Model / Dynamic Equation.
*
Select the instruments in Model / Select Instruments
*
To compute the first-stage estimates (equivalent to regular IV/GMM)
give the Actions / Multi-Stage GMM command.
*
To compute the second-stage estimates, using the first-stage estimates to
construct the required residuals, give the Actions / Multi-Stage GMM
command a second time, before any other command.
*
To iterate the procedure, repeat the last command as often as required.
Notes
1.
Giving any other estimation command (for example, Actions / Run
Estimation, or the "Run" button) resets the program, so that the next
Actions / Multi-Stage GMM command yields Stage 1 again.
2.
It may be possible to iterate the procedure to "convergence", so that no
further change in the estimates occurs. However, this procedure does
not optimize the GMM criterion function.
3.
This option is not available for IV estimation from the Model / Linear
Regression dialog.
6.8 Actions / Compute Test Statistic
Opens a sub-menu listing test options
*
Specify Score (LM) Test…
*
Specify Moment (M or CM) Test…
*
LM Tests of Parameter Restrictions
120
*
*
*
Wald Test of Set Restrictions
Specified Diagnostic Tests
Bootstrap Test of I(0)
Notes
1.
By default, the statistics printed by selecting these options are
asymptotically Chi-squared with degrees of freedom indicated in
parentheses. The nominal p-values of the tests are shown, enclosed in
braces, following the statistic values.
2.
The option of printing the "F form" of the tests, with associated p-values
from the F tabulation, can be selected with the checkboxes in the relevant
dialogs.
Note: In most cases the F form is to provide an alternative
approximation to the asymptotic Chi-squared distribution. These
tests are exact only in special cases.
SCORE (LM) TEST
3.
This option opens a dialog to allow specification of a test of the significance
of additional regressors selected from the data set. Radio buttons allow
selection of location of the test variables, either the Conditional Mean model
(Equation (1), included as variables of Types 1, 2 or 3) or the Conditional
Variance model (Equations (2)/(3), included as variables of Types 1, 2 or 3).
4.
If the selected Type is assigned to include one or more lags (see Model /
Dynamic Equation or Model / Linear Regression, and Model / Conditional
Variance) then the same number of lags of the test variable(s) are included in
the test set. It is not necessary for the null (estimated) model to contain lags.
Just set the number of lags required (for the relevant Type) with the Lags
scrollbar in Model / Conditional Mean or Model / Conditional Variance.
The degrees of freedom of the test are 'number of test variables x (1+ number
of lags)'. Select the "F form" of the test with the checkbox.
5.
There are two ways to run the test. Pressing "Go" will execute it immediately
using the currently stored parameter values. Otherwise, the test will be
performed following the next estimation run. To cancel the test, press "Clear".
MOMENT (M or CM) TEST
6.
This options opens a dialog to allow specification of a moment test of the
correlation of variables selected from the data set with either
*
the model residuals, or
*
the squared model residuals.
7.
If the Conditional Moment Test option is selected, the joint covariance matrix
of scores and moments is computed using the Robust formula (see Options /
Tests and Diagnostics). If the Moment Test option is selected, the selected
HAC formula is used to compute this covariance matrix. This selection
implies that serial correlation is permitted under the null hypothesis.
Select the "F form" of the test with the checkbox.
6.
Perform the test immediately with the current values by pressing "Go".
121
Otherwise it will be performed following the next estimation run. Cancel it by
pressing "Clear".
LM TESTS OF PARAMETER RESTRICTIONS
7.
By default, this option computes the LM test of the "fixed parameter"
restrictions in the current model, if any are set.
CAUTION: this test requires that the stored parameter values have been
estimated subject to the set restrictions. Otherwise it is invalid! It is
safer to run the test by checking the "LM Tests of Parameter Restrictions"
checkbox in Options / Tests and Diagnostics, and then run the estimation
of the model. The test is then reported automatically.
8.
If the model has been estimated subject to parameter constraints set up
through the Model / Parameter Constraints and Values dialogs, (select
the option "Restricted Estimation") then the LM test is performed on these
constraints, ignoring any fixes. This allows the option to be used to test
restrictions while other parameter fixes are in force.
Note: Parameters cannot be simultaneously fixed and subject to
constraints. Uncheck any fixes on "constrained" parameters, before
running the test
WALD TEST OF SET RESTRICTIONS
9.
This option does not open a dialog, but simply computes the test of the
constraints currently specified in Model / Constraints and the Values dialogs.
The option allows new constraints to be tested on the current estimated
model without re-estimation. If no constraints are specified, it does nothing.
SPECIFIED DIAGNOSTIC TESTS
10.
This command evaluates the optional tests that have been specified in the
Options / Tests and Diagnostics dialog. These are computed automatically
following an estimation or evaluation run, but this method allows additional
tests to be computed without generating the complete estimation outputs.
TEST FOR I(0) DEPENDENT VARIABLE
11.
This option simulates the model currently stored and computes Breitung's
(2002) statistic for the partial sums. The reported Kolmogorov-Smirnov
statistic compares the bootstrap distribution of this statistic with the same
statistic computed for the corresponding i.i.d. shocks. Its object is to
check whether the model dynamics are compatible with sample averages
adequately approximating their asymptotic distributions, in the selected
sample size.
12.
The I(0) test is for single equation models only, and is properly intended for
use with univariate time series models. If the equation contains exogenous
variables, these are held conditionally fixed in the simulations. If they are
nonstationary, this will in general yield a case of the alternative hypothesis.
13.
Choose a number of replications large enough to validate the asymptotic
tables from Smirnov (1948) - say 500. Set the number of replications in
Options / Simulation and Resampling, after checking the "Inference by
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Resampling" checkbox to activate the replications scrollbar.
NOTE: This checkbox does not activate the test itself. It can be
unchecked again after the setting is made.
6.9 Actions / Compute Forecasts & IRs
These commands generate and display either ex-ante forecasts or impulse
responses after a model has been estimated. Specify the outputs required in
Options / Forecasts.
Notes:
1.
If outputs are specified prior to giving the 'Run Estimation' or 'Evaluate
at Current Values' commands, they are computed automatically as
part of the run and printed along with the other outputs. These options
allow results to be generated, according to the current settings, without
re-running the estimation.
2.
"Ex ante forecasts" are generated using only exogenous variables and
observations pre-dating the forecast period. Multi-step forecasts are
computed recursively. Closed models, including models depending on
deterministic trends, can be forecast beyond the range of the available
data set.
3.
Tabular outputs are printed in the results window if this option is
selected in Options / Output and Retrieval..., "Print in Results Window".
Caution: This option is selected by default. If it is deselected, these
commands may appear to have no effect!
4.
Plots are displayed automatically as the commands are run, if this option
is selected in Options / Forecasting... They can also be generated
subsequently with the commands Graphics / Ex Ante Forecasts >
and Graphics / Impulse Responses >. These commands are disabled
(greyed out) if no outputs are available for display.
6.10 Actions / Retrieve Series
This command adds items such as residuals, fitted values, conditional variances,
switch probabilities and other generated series to the data set. To use it, first
open the Options / Output and Retrieval dialog and check the items to be
retrieved.
Notes:
1.
A fitted model must be present in memory when the command is given, or else
it has no effect. Either an estimation run has previously been performed, or a
previously stored model has been loaded using the Model Manager.
2.
When the Retrieve command is given, the checks in the Options / Output and
Retrieval dialog are removed so that the same items are not saved twice.
3.
Items can be retrieved automatically following a run by checking them in
the Options dialog before launching the run. Choose from the "Once" and
"Always" options in this case. The former removes the checks after saving.
123
6.11 Actions / Simulate Current Model
This selection generates and displays a stochastic simulation of the current model.
The user is prompted to choose to discard the series after viewing or write to the
data set and, in the latter case, to either add the series as new variable(s), or
over-write the existing dependent variable(s).
Notes:
1.
To select the mechanism generating the artificial shocks, see Options /
Simulation and Resampling Options. The choices are Gaussian, model
(according to likelihood function adopted) and a bootstrap of the current
model residuals.
2.
Create model for simulation in one of three ways: estimate a model, retrieve
a stored model, or type parameter values direct into the Values dialogs.
3.
A dependent variable (or variables) for the simulated model must exist in the
data set, and provides fixed pre-sample values when these are specified in a
dynamic model. This series can be optionally over-written by the simulation,
or the latter can be appended to the data set under a new name. In the
latter case, the conditional variance series is also appended if this is
generated in (e.g.) a GARCH or Markov-switching model.
4.
To bypass the discard/save prompts, assign this command to one of the
two user-selectable toolbar buttons (see Options / General). When the
button is pressed most recent choices are applied automatically. Use the
menu command to change them.
5.
To simulate without a data set loaded, first use the 'Extend Sample' option in
Setup / Data Transformations and Editing to specify the sample size required
Then create a placeholder variable using 'Make Zeros'.
6.
If estimation is by least squares or GMM, the residual variance is not in the
parameter set, and is estimated extraneously from the residuals. If simulation
follows estimation, the current estimate is used. To specify a model for
simulation without prior estimation, select one of the conditional maximum
likelihood (time domain) estimators. This will allow all the model parameters,
including the error variance, to be entered in the Values dialogs.
7.
It is possible to simulate equations in which the generated random shock
enters nonlinearly, using the Coded Equation option. See Model / Coded
Equations and General / Entering Formulae for details. Such equations
cannot be estimated in this form, but must be coded separately.
8.
A related option implemented through coded equations is to replace
one or more data series by columns of standard normal random drawings
before a simulation is run. This facility allows simulation experiments under
"random regressor" assumptions without formulating a multi-equation
model. See Model / Coded Equations and General / Entering Formulae for
details.
124
PANEL DATA
9.
To simulate panel data, a formatted panel data set must be loaded so that
the program is in "panel data mode". Shocks can be generated either as
bootstrapped residuals or as Gaussian pseudo-random variates. In the latter
case, the "within" and "between" variances are set in the Model / Panel Data
dialog. Random effects are produced by setting the "between" variance
to a positive value.
Note: the "within" variance" setting overrides the variance setting in Options
/ Simulation and Resampling.
10.
In the residual bootstrap option, individuals are drawn randomly with equal
probability, and then the dated observations are resampled from the residuals
for the selected individual, using the resampling scheme selected in Options /
Simulation and Resampling.
11.
The Data Transformation settings in Model / Panel Data are ignored in
simulations. The actual data are simulated, using the actual exogenous
variables.
12.
Systems of panel equations can be simulated. However, if the Gaussian
shocks option is adopted, in this release all equations have the same
variances, as specified in Model / Panel Data, and zero covariances.
6.12 Other Commands
SET DEFAULT VALUES
This command sets all free parameter values to defaults. Fixed values, and all fixes,
bounds and constraint settings, are retained.
CLEAR VALUES
This command has the same effect as pressing the Clear button in all the Values
dialogs. Parameter values are set to defaults, and all fixes (except defaults), bounds,
and constraints are removed.
CLEAR RESULTS WINDOW
If the results buffer becomes full and will accept no more text, use this command to
clear it. Note that its contents can first be first saved to a file, see File / Results / Save
Selected Text.
CLOSE ALL DIALOGS
This command is given automatically before estimation operations are carried out.
Current window positions are stored.
RESTORE DIALOGS
Reverses the action of Close All Dialogs. Use it after an estimation run, and also
after starting the program, to restore the previous window configuration. This action
can optionally be made automatic, see Options / General Options.
RESET DIALOG POSITIONS
Resets the stored horizontal and vertical screen positions of all dialogs to (0,0),
relative to the main window. This command is useful in case dialogs get "lost" from
125
the visible screen area, which can happen if program settings are transferred
between machines different screen resolutions.
Notes:
1.
The actions of Close All Dialogs and Restore Dialogs are duplicated by the
toolbar "Windows" button, which toggles between them.
2.
Dialog positions for open dialogs are saved between runs. Restore Dialogs (or
the "Windows" button) restores your dialog configuration at shut-down.
126
7. Graphics
7.0 Graphics: General Information
Graphics are displayed in a window whose size is linked to screen resolution.
As many graphs as desired can be open at once. Close them by clicking the
"Close" button in the top-right hand corner, or from the Windows taskbar.
*
Clicking on the "gnuplot" icon in the top-left corner of the window opens
a context menu. Choose "Options" to open a submenu of useful commands.
These include changing the text font, line style and background colour,
sending to a printer, and copying the graph to the Windows clipboard, so
that the image can be pasted into your favorite graphics program.
*
For bitmaps, IrfanView is a highly recommended freeware package, which
can convert an imported image to a variety of bitmap formats such as .gif,
.png and .jpg. Note that the gnuplot window can be resized by dragging the
corner with the mouse, and a saved bitmap image will have the same
dimensions. Alternatively, pasting the clipboard into a graphics program such
as CorelDraw results in a vector graphics image that can be edited further,
and saved in various formats.
*
An alternative procedure to save a graph is with the command File /
Graphics / Save Last Graphic. Select the type of file to be saved in
Options / Output and Retrieval. The desired line and text characteristics
as well as bitmap dimensions can be selected in Options / Graphics.
Note that Postscript vector graphics formats (.eps or .epc) can also be
imported into graphics programs such as CorelDraw for further editing.
7.1 Graphics / Show Data Graphic
Opens a dialog for selection of graphical representations (time plot, correlogram,
partial correlogram, spectrum, histogram and normal QQ-plot) of any variable in
the data set.
SIMPLE PLOTTING
*
Select the type(s) of plot required, using the check boxes.
*
Select one or more names in the variable list.
*
Optionally select for the series to be either detrended by OLS, or
differenced, before plotting.
*
Press "Sample ..." to open the Set Sample dialog and choose the sample
required.
*
Press "<<< Plot >>>". Alternatively, just double-click the name of any series
(convenient for a single plot).
*
Press "List" to display the the currently selected sample in spreadsheet
format.
127
Notes:
1.
Unselect a selected variable by clicking it second time. Press 'Clear' to
unselect all selected variables.
2.
Double-clicking a variable on the list just displays the plot. Selecting with a
single click and then pressing 'Go' plots the variable(s) and leaves them
selected.
3.
Three modes of display are available for time plots, correlograms and
partial correlograms, spectra and QQ-plots. The mode is selectable by
the radio buttons in the Options / Graphics dialog:
*
"Individual": each variable plotted in its own frame.
*
"One Frame": multiple individual graphs in one frame.
*
"One Graph": multiple series plots overlaid in one graph, with
common axes.
4.
In "Individual" mode, multiple representations of a series (e.g. time plot,
correlogram, etc.) are still displayed in one frame. Draw these
separately to get them in their own frames.
5.
In "One Frame" mode, up to 36 graphs can be displayed in one frame.
However, with a large numbers of plots the quality of the display on a
standard monitor is not too good.
6.
In "One Graph" mode, line colours and styles are assigned according
to the line style selections in Options / Graphics, variables being ordered
by their position in the list. For more flexible assignment of styles, see
"Multi-series Plotting" below. This mode is not available for Histogram/
Density plots, if these are selected the mode defaults to "One Frame".
7.
If either the Scatter Plot or Bivariate Density options are selected, the first
two highlighted variables in the list are plotted together - the first on the list
is assigned the 'vertical' axis, (Y) and the second the 'horizontal' axis (X).
Reverse the ordering, if desired, in Setup / Data Transformation and Editing
/ Edit / Move Up-Move Down. If only one variable is highlighted with these
options, nothing is plotted. Other options can be selected at the same time,
and will be displayed for all highlighted variables.
8.
By default, T/2 correlogram and partial correlogram points are plotted,
where T is the length of the selected plotting sample. Optionally, the
number of points to be plotted can be set in the Setup / Compute
Summary Statistics dialog. The effective number of plotted points is the
minimum of T/2 and this selection, provided if it is greater than zero and
the option is selected.
NOTE: Only the correlogram order is selected by this option. To plot the
actual points listed in Setup / Compute Summary Statistics, the
samples selected in the two dialogs must match!
9.
In a scatter plot, the two regression lines (Y on X and X on Y) are
superimposed by default. Note that these both pass through and jointly
128
indicate the point of sample means. The more nearly parallel these are,
the higher the correlation between the variables. Unselect this feature
in Options / Graphics.
10.
Plotting options for the bivariate density can be selected in Options /
Graphics. The options that can be selected are
*
Contour/Surface/Both in "3D Plot Type",
*
Density, Histogram and Normal in "Distribution Plot Options".
11.
The sample of observations selected for plotting (Sample 5) is independent
of the samples set concurrently for other program functions. See Setup
/ Set Sample for details. If data are missing for part of the specified period,
nothing is plotted for these observations.
MULTI_SERIES PLOTTING
This option allows up to 8 series to be plotted on one graph with line styles
selected by the user. All the series representations except Histogram/Density
and the bivariate plots can be drawn using this option. It gives the user more
control over plotting styles, and allows multiple series plotting without changing
the basic setting in Options / Graphics.
*
Check the "Multi-Series Plot" Checkbox.
*
Choose a line style (1-8) using the radio buttons, and then a variable
from the list - at most one variable can be selected for each style.
*
Repeat for up to 8 series.
*
Press 'Go'.
Notes:
13. The 'Centre' and 'Standardize' checkboxes allow the variables to be
relocated and rescaled for comparability. Centre subtracts the mean, and
Standardize also divides by the standard deviation.
14.
The 'RH Scale' checkbox is enabled when two or more series are selected.
If checked, the series with the largest line number is plotted
against the right-hand axis. If more than two series are selected, all the
others are plotted against the left-hand axis as usual.
15.
The 'C-Bands' checkbox enables the option of drawing 2SE confidence
bands around a series, based on a companion series of standard errors.
Either one or two series can have confidence bands. These must be
assigned to positions 1 and 3, and the companion series must be assigned
to positions 2 and 4 respectively. Positions 5 to 8 can be assigned to
additional series in the usual way.
Note: If the designated 'standard error' series contain negative values,
an error message is shown.
16.
If the line type for Line 8 is chosen as 'Band Fill', the selected variable
is used to divide the sample into 'regimes'. If the selected variable is
129
positive the regime is "On", and if the selected variable is zero or
negative the regime is "Off". The observations of the "On" regime are
indicated by light gray shading in the plot. Typically, the indicator
variable would be a zero-one dummy.
NOTE: Only Line 8 can be given the Band Fill style.
LISTING
17. The 'List' button invokes the data spreadsheet that is also accessible from
Setup / Data Transformation and Editing, although here editing functions
are suspended. It simply allows a view of the values of the plotted points.
The sample listed matches the plotted sample.
7.2 Graphics / Equation Graphics
The following items can be plotted following an estimation run:
*
'Actual and fitted' series (submenu, time and scatter plots)
*
Residuals (sub-menu)
*
Variance-adjusted residuals (sub-menu)
*
Conditional variances (GARCH and regime switching models only)
*
Regime probabilities (sub-menu, regime switching models only)
*
All the time plots for the model in one frame.
*
Equilibrium relations (sub-menu, error correction models only)
*
Ex ante forecasts (sub-menu)
*
Solved moving average coefficients, impulse response and step response
(submenu)
*
A 2D or 3D plot of the criterion function if computed, see Actions / Plot
Criterion Grid.
*
Plots of the recursive or rolling estimations, if computed (dialog)
*
Kernel density plots of the bootstrap distributions of parameter estimates
and test statistics.
Notes:
1.
In the Residuals, Adjusted Residuals and Equilibrium Relations submenus,
the available options are time plot, correlogram, spectrum, correlogram
and spectrum of absolute values, histogram and kernel density, and
normal QQ-plot. There is an option to display all the representations in
the same frame.
2.
The Actual vs. Fitted scatter plot includes the "Fitted vs. Fitted" line, which
has slope 1 by construction and passes through the point of sample means.
The residuals correspond to the vertical deviations around this line, but
ordered by magnitude of the fitted values instead of the sample time ordering.
3.
Regime probabilities are summed over lags in Hamilton's switching model.
Smoothed regime probabilities are computed by Kim's algorithm, see
Kim and Nelson (1999), pp68-70. When switching probabilities are
explained by exogenous variables, the variable transition probabilities can
be plotted; more precisely, the plotted series are the simple averages over i
of the probability of jumping from regime i to regime j, at time t.
For smooth transition models, the transition function can be plotted.
130
4.
Forecasts and solved MA weights can be computed for the equation and
the conditional variance, where this is estimated.
5.
The interpretation of ex-ante forecast time plots depends on the
forecasting method. With analytic forecasting, the plots show the estimated
mean forecast, with optional 2-standard error bands. Standard errors are
not available for bilinear models and user-supplied dynamic models, nor
for conditional variance forecasts in GARCH models.
6.
Monte Carlo forecasting generates the distribution of stochastic simulations,
and the plots show the median forecast and the 2.5% and 97.5% percentiles.
These therefore define a true 95% confidence band, regardless of the error
distribution, and are available for all models, and for conditional variances.
Kernel density plots of the empirical forecast distributions are also available
for any point in the forecast period (selected in Options / Forecast and
Simulation Options).
7.
To change the type or number of forecasts, make the desired selection in the
Options / Forecast and Simulation dialog, then recompute the model, using
either Actions / Run Estimation, or Actions / Evaluate at Current Values to
avoid re-estimating.
8.
To view a plot of the recursive/rolling estimations, either double-click a
parameter/statistic in the list, or select it and press "Go". The rolling
parameter estimates are displayed with 2-standard error bands (the
usual regression standard errors, with covariance matrix formula
selected in Options / Tests and Diagnostics.)
9.
The 'Fill' symbol option is used for probability and variance plots. That is,
the region between the plotted line and the time axis is shaded light gray.
If for any reason a different plot style is required for these series, use the
"Retrieve Series" command to add them to the data set, then plot using the
options in Graphics / Show Data Graphic.
10.
Select the type of plot desired for confidence and standard error bands in
forecasts and recursive/rolling estimation (none, bands or bars) in Options
/ Graphics Options.
7.3 Graphics / Monte Carlo Graphics
The frequency distributions generated by Monte Carlo experiments can be
displayed as kernel densities and histograms. Cumulative frequencies can also
be displayed as an option.
*
Select plots for display by clicking on the list, or pressing 'Select All'.
Unselect an item by clicking again. Remove all selections with 'Clear'.
Plot selected items by pressing 'Plot'.
*
Double-clicking a list item displays the plot, but does not leave the
131
item highlighted.
1.
The graphic display dialog opens automatically at the completion of a
Monte Carlo run. Alternatively, open it from the menu with Graphics
/ Monte Carlo Distributions...
2.
The bandwidth used to compute the kernel density is user-selectable.
Initially it is set to the default value, displayed as '1' on the scrollbar.
Move the scrollbar to change the ratio of the bandwidth to the default,
then redisplay the plot to see the effect. The chosen value is stored
with the distribution data and used the next time the distribution is
plotted, as shown by the scrollbar.
3.
If the scrollbar setting is changed by the user, the new value is used
for the next plot, and replaces the stored value(s) for the distribution(s)
plotted.
Tip: to avoid changing a stored bandwidth after moving the scrollbar,
close and re-open the dialog before giving the Plot command.
4.
Monte Carlo graphics are stored in the .TSD file created with the Data
Generation Model. If the .TSD file is present, reloading this model makes
the results and plots of the last experiment performed with this model
available to view, just as when the model was run. To save these outputs
separately from the model, give the command File / Listings / Save
Listings File, and enter a file name in the file dialog.
5.
The distributions from a simulation run can be stored in an EDF file to
supply critical values for tests. The currently stored bandwidths for each
distribution are used to compute the EDF kernel densities.
Note: EDF file creation can also be done automatically, using the default
bandwidth, by setting the requisite option in Setup / Monte Carlo
Experiment. The present option can be used to fine-tune the
bandwidths used for each distribution, if required.
6.
Monte Carlo graphics can be stored and displayed independently of the
DGM that produced them. This allows the results of different runs to be
plotted together for comparison.
*
Highlight the plots to be stored.
*
Click on "Add to Store".
*
In the text box that opens, the current name is displayed. Edit or
replace this name to identify the plot in a comparison of DGMs.
*
Click "OK", or press the Return key, to close the text box.
*
Repeat the naming procedure for each plot selected.
Note: The stored plots are saved in the settings file, not in the .TSD file
associated with a model.
7.
To display the stored plots, select Graphics / Stored MC Distributions ... from
the menu.
*
Select and display plots as usual
132
*
*
*
Highlight a name and click "Rename" to re-open the text box and
type a new name.
Note: Only one plot at a time can be renamed.
Highlight any number of names and click "Remove" to remove the
graphics from the store.
Highlight one name and click "Move Up" or "Move Dn" to change
the order in which plots are displayed
Note: The bandwidths for stored plots can be changed in the same way as
described in 3.
8.
To show two or more density plots in the same graph for comparison
select the Options / Graphics from the menu and then "One Graph" in Multiple
Series Display. The MoveUp/Dn buttons allow control over the colours or
line types used to display each plot, also the order in which legends appear.
Note: Histograms are not displayed for two or more densities in the same
graph, even if this option is selected.
9.
The saved plots can be exported to a spreadsheet file, for subsequent
reloading and/or merging with those stored in a different settings file. Pressing
the "Save Plot Data" button opens the file dialog for saving.
Notes:
*
Reload plots with the command File / Data / Load Tabulations /
Density Plot File.
*
File names with the prefix "DNS_" are recommended. Such files
can be loaded quickly using drag-and-drop.
*
The spreadsheet format is as follows:
Row 1:
Plot names.
Row 2:
Kernel bandwidth index (integer 0-32)
Row 3:
Initial bin ordinate.
Row 4.
Increment (bin width).
Rows 5,....
Histogram values.
133
8. Options
8.0 Options: General Information and Defaults
By default, only one Options dialog is open at a time. Opening a second dialog
causes the first to close. This behaviour is optional, see General Options.
The <<< and >>> buttons at the top of each window allow easy navigation between
the options dialogs. Pressing them opens the next/previous options dialog, so that
current program settings can be reviewed rapidly.
DEFAULTS
The default settings are as follows. These are selected if the file "settings.tsm" is not
found in the working directory at start-up, or on the command File / Settings / New.
"*" in the left-hand column indicates that this setting is stored with a model,
and hence is liable be changed when a model is loaded.
Output and Retrieval Options:
Save Data to Files of Type .
Export Listings to Files of Type
Save Listings Automatically. .
Print in Results Window
.
Retrieve Generated Series
.
.
.
.
.
.
.
.
.
.
.
XLS
None
No
Correlograms
Once
Test and Diagnostics
*
Q Test Order .
.
.
*
Q-Test Type .
.
.
*
LM Tests
.
.
.
*
Durbin Watson Test .
.
*
Diagnostic Tests
.
.
*
Covariance Matrix Formula .
*
Kernel for HAC Covariances .
*
Bandwidth for HAC Covariances
.
*
Show Residual Moments
.
*
Show Log-Likelihood & Criteria
*
Tests in R^2 Form
.
.
*
Use EDFs
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
12
Box-Pierce
No
No
None
Robust
Parzen
[n^(1/3)] for Bartlett,
[n^(1/5)] otherwise.
Yes
Yes
No
No
Forecasting Options
*
Forecast Type. .
.
*
Forecast Method
.
*
# Actuals in Forecast Plot
*
# Monte Carlo replications
*
Compute Confidence Bands
*
Impulse Responses .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Ex Ante Multi-step
Analytic
50
1000
Yes
Impulse
Simulation and Resampling Options
*
Shock Distribution .
.
.
.
Gaussian
134
*
*
*
*
*
*
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0 (system clock)
1
Fixed
No
Yes
No
Once
Equal Tails
99
No
No
No
50
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.PNG
No
Yes
YYYY
640x480
Bands
One Frame
Lines
Both
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Yes
No
.No
Colour
No
No
Yes
1
1
ML and Dynamic Options:
Maximum ARMA/GARCH Order .
*
MA Polynomial with '+'s
.
.
*
Root of Student t d.f. .
.
.
*
Log of Skewness Parameter .
.
*
Restrict Pre-Sample Lags
.
.
*
GARCH coefficients in Standard Form
*
Type 2 GARCH intercept
.
.
*
Root of GARCH Intercept .
.
*
No. Gauss-Seidel Its in GARCH-M .
*
GARCH-M Trimming Factor .
.
*
Compute EGARCH Likelihood by G-S
*
No. G-S Its. to compute EGARCH .
.
.
.
.
.
.
.
.
.
.
.
.
10
No
2
Yes
No
No
No
2
5
10
No
50
Optimization and Run Options:
*
Report Minimand
.
.
No
*
*
*
*
*
*
Random Number Seed
Shock Variance (Gaussian)
Presample Data
type I fractional
Use Likelihood Model
Enable Bootstrap Inference
Once/Always .
.
Confidence Intervals .
Bootstrap Replications
Fast Double Bootstrap
Bias Correction
Newton-Raphson algorithm
Maximum Iterations .
.
.
.
.
.
.
Graphics Options:
Export Graphs to Files of Type
Save Graphs Automatically .
Display plots using GnuPlot .
Dates Format .
.
.
PNG Image Size
.
.
2SE Band Style for Forecasts .
Multiple Series Display
.
Time Series Plot Type .
.
Criterion 3D Plot Type
.
Density Options:
Histogram
.
.
Normal Curve .
.
CDF
.
.
Colour/Monochrome
.
Keep PLT files
.
Extended Actual-Fitted
'Fill' Probs and Var plots
.
Line Width
.
.
Symbol Size
.
.
.
.
135
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
10
3
-1 = Ox Default
0
-1 = Ox Default
-1 = Ox Default
0 (= off).
Yes
500
5
0.85
10
General Options:
Restore Dialogs Automatically
.
Enable Savings Prompts
.
.
Store Model After Each Run .
.
Delete Temporary Files on Exit
.
Automatically Close Options Dialogs
Size of Results Window Text .
.
Echo Results to Console
.
.
Show Tool Tips
.
.
.
Enable Error Recovery
.
Drag-Selection
.
.
Enable Optimization Estimators
.
.
.
.
.
.
.
.
.
.
.
No
Yes
No
No
Yes
12 points
No
Yes
Yes
Yes
Yes
*
*
*
*
*
*
*
*
*
*
No. Grid Points for Criterion Plot
Absolute bound on dynamic params.
Max No. of BFGS Iterations
Iteration Print Frequency
.
Strong Convergence Crit.
.
Weak Convergence Crit.
.
Parameter Rescaling Factor .
Simulated Annealing
.
# SA Iterations
.
Initial Temperature .
.
Temperature Reduction Factor
# Iterations before Temp. Reduction
8.1 Options / Output and Retrievals ...
SAVING DATA FILES
1.
The type of data file saved (.XLS, .XLSX., CSV, .WKS, .IN7, .DAT
or .MAT) is determined by the extension added to the file name. If no
extension is added by the user, the one selected in this dialog is included
automatically. However, note that the user's choice over-rides the selection
in this dialog. For example, if the name is selected from the list of existing
files in the file dialog, with extension .XLS, the selection here is ignored, if
different.
EXPORTING AND PRINTING LISTINGS
2.
Select a radio button for the type of spreadsheet file or ASCII file to be
saved by the command File / Listings / Export Spreadsheet. By default
the files are identified by a descriptive name and the current run ID.
3.
Check the checkbox "Save Listings Automatically" to have all the series
associated with an estimation run saved to a file of the selected type. If this
box is not checked, specific outputs from the latest run can be saved
individually as required, by selecting the menu items under File / Listings /.
4.
To distinguish sample and ex-post forecast periods in the output file, an
extra column is printed with an indicator variable, 0 = sample, 1 = forecast.
136
5.
Check the boxes in "Print to Results Window" to have the items appear
on the screen. Large screen listings are best avoided, since the results
window buffer may fill up rapidly.
EXPORTING GRAPHICS
6.
Graphics can be saved to file in both bitmap and vector graphics formats.
PNG and GIF are standard bitmap formats, providing an exact image of
the displayed window in the dimensions specified (see 8.5 Options /
Graphics).
EPS (Encapsulated PostScript) and EMF (Enhanced MetaFile) are vector
graphics formats. Vector graphics can be edited in drawing packages such
as Corel Draw.
PNG, GIF, EPS and EMF files can all be loaded directly into Word and
TeX documents.
They can also be viewed and converted into other formats, such as JPEG,
using freeware packages such as the recommended IrfanView.
FIG is another vector graphics format. FIG files can be viewed and edited
in the WinFig (Windows) and XFig (Unix) shareware packages.
7.
If the checkbox "Export Graphs Automatically" is checked, every graph
is saved to disk in the chosen format, at the same time it is displayed.
Otherwise, the menu item File / Graphics / Save Last Graphic saves the
graph most recently displayed.
8.
.GWG (GiveWin format) files are created if the compiler directive
#DEFINE OXDRAW appears in the run file. This option loads the
OxDraw graphics package, and disables GnuPlot, so display within the
program is not available. The format settings in this dialog are ignored.
See Appendix B of the main documentation for more details.
OUTPUTTING TABLES
9.
Items that can optionally be printed to the output include the forecasts
and impulse responses, residual correlograms, the parameter covariance
matrix, the gradient vector and its covariance matrix, and the Hessian
matrix of the estimation criterion.
10.
Ex ante forecasts are tabulated together with either standard errors of
forecast or 95% confidence bounds, depending on the option selected in
Options / Forecasting. If ex ante forecasts are computed for periods for
which some or all of the the actual data are available in the data set, so
that forecast errors are known, the root mean square of the forecast errors
is shown beneath the table.
11.
The gradient and Hessian may have diagnostic uses.
*
The gradient is displayed only for iterative estimators, in the cases
where either the optimization algorithm fails to return the state
"Strong Convergence", or the output is evaluated at the current
point, without optimizing.
*
The covariance matrix of the gradient is not computed when the
standard covariance matrix formula is selected in Options / Tests
and Diagnostics.
137
*
12.
In ordinary least squares, the Hessian is evaluated as the matrix
of sums of squares and products of the regressors divided by the
residual variance
The grid of criterion values following a call to Actions / Plot Criterion
Grid can be optionally printed to the results window, provided this
checkbox is checked first. The results can also be displayed graphically
and exported to a spreadsheet, and these latter options can be
effected after running the estimation.
OUTPUTTING SERIES
13.
The following series can be either printed in the results window, or
exported to a file.
*
The actual data series, Y_t.
*
The fitted series Yhat_t, followed by the ex post 1-step forecasts,
if specified.
*
The residuals Y_t - Yhat_t (solving equation (1) for u_t at the
estimated parameters) followed by ex post 1-step forecast errors,
if specified.
If conditional heteroscedasticity options are selected, also
*
The variance-adjusted residuals , followed by ex post 1-step
adjusted forecast errors, if specified.
*
The estimated conditional variances, followed by ex post 1-step
variance forecasts, if specified.
If a smooth transition model specified, also the transition weights.
If Markov-switching regimes are specified, also
*
The filter probabilities
*
The smoothed probabilities
*
For explained switching models, the transition probabilities for
Regimes 1 to M-1.
In regime-switching models the residuals are computed as weighted
averages of the regimes, using the filter probabilities as weights.
Note: In the case of the Probit model, generalized residuals replace
variance-adjusted residuals.
RETRIEVING GENERATED SERIES
14.
"Retrieving" series means adding them to the current data set for further
analysis in the program. The radio buttons allow you to choose whether
to retrieve the next run only, and then cancel the option, or keep it
selected. The series are allocated standard names, with numbers
appended to distinguish successive retrievals. They can be renamed
more descriptively in the Data Transformations dialog, if desired.
8.2 Options / Tests and Diagnostics ...
CORRELOGRAM POINTS
The scroll bar controls the number of correlogram points to be computed
when this option is selected in Options / Output and Retrieval. The upper limit
is set at (number of observations)/3.
138
The first two checkboxes, which are checked by default, control the display of
various standard statistics following an estimation run. Unchecking these boxes
simplifies the estimation output, which may be appropriate for elementary
tutorial use.
LM TESTS OF SET RESTRICTIONS AND "FIXED" VALUES
Check the "LM Tests of Parameter Restrictions" checkbox to compute the
score (LM) statistic for the validity of restrictions imposed on the parameters in
the "Values" dialogs.
There are two modes of operation of this option.
*
If parameter constraints have been activated in the Parameter Constraints
dialog with the option "Restricted Estimation" selected, these restrictions
are tested.
*
If not parameter constraints are set, but parameters have been "fixed" in
the Values dialogs, a test of the fixing restrictions is generated.
Notes:
1.
In first case, parameter fixes are not tested. This allows testing one set
of restrictions while simultaneously including other restrictions in the
maintained hypothesis.
2.
These tests can also be computed for a fitted model with the option
Actions / Compute Test Statistics / LM Tests of Parameter
Restrictions
3.
This option is not available for linear regressions. Use Wald tests to
test restrictions in this context.
FORM OF THE LM STATISTICS
The 'T.R^2 form' option gives a choice of small sample approximations for
diagnostic LM tests on the mean model. The default is to report the statistic
W/(1 - W/T), where W is the usual LM statistic, and T is the sample size.
If W takes the usual form of TR^2 in the artificial regression of the residuals
on the gradients under H0, the default is therefore TR^2/(1 - R^2). In a
linear model, this is equivalent to normalizing the statistic with the unrestricted
residual variance under the alternative. The asymptotic distributions are the
same under H0. Check the option to report W itself. When the 'F-form' of
the statistic is selected, this option is unavailable.
LAGS FOR THE ADF AND ERS TESTS OF I(1)
These tests for the integration order of series are accessible in the Setup /
Compute Summary Statistics dialog. The number of lags to compute the
statistic can be chosen either manually using the scrollbar, or automatically
using a model selection criterion selected in the right-hand panel of this
dialog.
4.
The 'ADF Lags' scrollbar is disabled unless the "No Criterion"
option is selected.
5.
The ADF lags can also be set in the Model / Linear Regression
139
dialog, when the "Cointegrating Regression" option is selected.
In this context, the setting is applied to the ADF-based test of
cointegration as well as the test of I(1). Note that the setting in
either dialog is mirrored in the other - the same internal counter
is set in either location.
DIAGNOSTIC TESTS
These options are presented in a separate dialog, accessible from this dialog
and also the Linear Regression and Dynamic Equation dialogs. The details
are given in Section 8.2a of this manual.
COVARIANCE MATRIX FORMULAE
Four methods of calculation are available for computing covariance matrices:
*
'Standard' corresponds to the information matrix in ML estimators, and is
generally appropriate for correctly specified models with i.i.d. errors.
*
'Robust' allows for mis-specified likelihoods and heteroscedastic but
independent errors.
*
'HAC' is for models with residual autocorrelation as well as possible
heteroscedasticity.
*
'KVB' selects the inconsistent estimator proposed by Kiefer, Vogelsang
and Bunzel (2000).
Notes:
6.
The method selected here is used for equation standard errors and also
Wald and LM tests. M statistics use HAC, and nonparametric tests of I(0)
(see Actions / Compute Summary Statistics) use HAC. Whittle estimates
use HAC if KVB is selected.
7.
The KVB estimates correspond to HAC using the Bartlett kernel and
bandwidth equal to sample size. Note that they are inconsistent, but yield
asymptotically pivotal tests based on a nonstandard distribution. P-value
inequalities are reported from the published tables, and are identified in the
output with the @ symbol .
NOTE: KVB can be implemented for nonlinear models and GMM at the
user's discretion, but take care to note that asymptotic distribution results
for these cases are not available to date. See the citations in the main
document for further details.
HAC KERNEL FORMULAE AND BANDWIDTH
The kernel formula selected here is used when the HAC covariance matrix is
selected. It also determines the choice for Phillips-Perron, KPSS and RS tests, and
Fully Modified Least Squares estimation. It does not effect the kernels used in
density
plotting and nonparametric regression, which are Ox defaults and cannot be changed
by the user.
There are three options for selecting the HAC bandwidth.
*
Manual selection using the scroll bar
*
The automatic 'plug-in' method due to Andrews (1991)
*
The automatic 'plug-in' method of Newey and West (1994).
The plug-in bandwidths are set as the minimum of the value returned by the
140
formula and (sample size)/2. Larger bandwidths can be set manually. Check the
'Prewhitening' checkbox to prewhiten the data by a VAR(1) regression, prior to
computing the HAC covariance matrix, V. V then is 'recoloured' as DVD' where
D = (I - A)^(-1) and A is the VAR coefficient matrix.
NOTE: Use prewhitening with caution! It may inappropriate, e.g., in construction of
test statistics for I(0), by overcompensating under the alternative.
MODEL SELECTION CRITERIA
A model selection criterion is needed for three automated model selection features.
*
Automatic regressor selection (see the Actions menu and Setup / Automatic
Model Selection).
*
Lag selection in the augmented Dickey Fuller test.
*
Lag selection in the Stock-Watson/Saikkonen augmented least squares
estimator for cointegrating relations.
The radio buttons allow a choice of the Akaike, Schwarz and Hannan-Quinn
criteria for these purposes.
SUPPLYING AN EDF FILE FOR P-VALUES
Check the box "Use EDF from File for p-Values" if tabulations of test distributions
has been created by Monte Carlo simulation of the null hypothesis. The currently
loaded EDF file is used to supply p-values for each test for which a tabulation exists
in the file. In the case of significance tests (t-tests) the parameter's name must match
a name in the file.
Notes:
8.
P-values taken from the EDF are marked with a '$' in the output.
9.
See Setup / Monte Carlo Experiments for details of the EDF file format.
10.
EDF files can be read and plotted in Setup / Look Up Tail Probability and
Setup / Look Up Critical Value. To read off a p-value, type the test statistic
into the first 'Tail Probability' dialog.
11.
EDF files are spreadsheet files. They can be loaded as data files, inspected
and merged in TSM.
12.
If tabulations for several sample sizes are created, these can be merged into
a single EDF file. Use the command File / Data / Tabulations / Merge EDF
File to merge a file on disk with the one resident in memory. These
tabulations will be used to calculate p-values by interpolation.
For example, suppose tabulations for T = 50, 100, 200 and 500
observations have been created and merged. If the actual T is 150, a
weighted average of the tabulated p-values is returned, with weight
w = ((200 - 150)/(200 - 100))^2 = 0.25
on the case T = 100, and 1 - w = 0.75 on the case T = 200
(i.e., greater weight on the larger sample size than with a linear
interpolation). If T exceeds the largest tabulated sample size or is less
than the smallest, then the nearest values are used with weight 1.
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8.2a Options / Tests and Diagnostics / Diagnostic Tests...
Tests selected in this dialog are calculated automatically following an estimation run.
They can also be computed independently using current estimation outputs from the
Actions / Compute Test Statistics menu.
The main preset diagnostic tests are available in score test and conditional moment
test versions. Unless otherwise indicated the statistics, by default, are asymptotically
Chi-squared with degrees of freedom shown in parentheses. The nominal p-values of
the tests are shown, enclosed in braces, following the statistic values. F-versions of
the tests can optionally be substituted, although note that these are not exact except
in special cases.
Q TESTS FOR SERIAL DEPENDENCE
Q tests for residual autocorrelation in levels and squares are printed after an
estimation run by default. The Box-Pierce (1970) formula is used by default.
Check the "Ljung-Box" radio button to use the Ljung-Box (1978) formula, or
"None" to disable this option.
Notes:
1.
The upper limit to the Q test order is set at (number of observations)/3.
2.
In models where variance-adjusted residuals are defined (GARCH, regime
switching), the Q statistics are computed for these series.
3.
When ARMA components are fitted, the degrees of freedom of the 'levels'
Q-test, as used for computing asymptotic p-values, are reduced by p+q
accordingly. No such adjustment is made in respect of fractional integration
models, nonlinear dynamics, GARCH models etc, where the required
corrections are generally unknown. The "nominal" p-value must be interpreted
with caution in these cases.
SCORE (LM) TESTS
The following pre-set score tests are available. In each case, the score of the
extended model at the null parameter values is tested. The extensions are:
*
Autocorrelation: lagged residuals in mean equation(s).
*
Neglected ARCH: lagged squared residuals in conditional variance
equation(s),
or lagged absolute normalized residuals, if EGARCH is specified.
*
Nonlinear Functional Form (RESET): Integer powers of the fitted values
of the null model in the mean equation(s).
*
Heteroscedasticity: square of the fitted values in conditional variance
equation(s).
*
White's heteroscedasticity test: squares and cross-products of the
explanatory variables in conditional variance equation(s).
*
AR common factors: p lags of Type 1 regressors in a model with AR(p)
errors specified.
Select the number of lags to be included and the order of polynomial in the fitted
values with the scroll bars. These statistics are indicated in the output by "(LM)"
after the description.
142
Notes:
4.
If no conditional variance is specified in the null model, the LM tests for
neglected ARCH and heteroscedasticity is performed by regressing
the squared residuals on the test variable(s). Otherwise, the test variable(s)
are added to the conditional variance model as regressors.
5.
The test variables are designated regressors of Type 3 if a MA (GMA)
component is selected, and of Type 2 if a AR or FI (GAR or FIGARCH)
component is selected, and otherwise of Type 1.
NOTE: Test variables cannot be assigned to a Type for which lags are
already selected. If lags are specified for Type 1 variables, the
test may be unavailable. A warning message is printed in this case.
6.
In the implementation of White's heteroscedasticity test, the possibility of
collinearity between the squares and products is allowed for automatically.
In this case, the principle components with positive eigenvalues are
extracted.
7.
The AR common factor test is enabled in the following case: a model
with Type 1 regressors, current values only; no Type 2 regressors;
and an AR(p) error process is specified, but not a fractional process.
The null hypothesis is that p lags of the regressors are not independently
significant, in other words that there are common AR factors shared by
the dependent variable and regressors in the model, so that AR errors
are valid representation of the dynamics.
8.
In multiple-equation models, the full set of test variables is added to each
equation of the model.
9.
LM tests are computed by creating an extended model with test
variables added to it. In some situations the resulting model is unidentified,
with a singular covariance matrix. In such cases the statistic cannot be
computed and is assigned the value ".NaN", standing for Not a Number.
CONDITIONAL MOMENT (CM) TESTS
Eight conditional moment tests are pre-set. The hypotheses under test are the
following.
*
Autocorrelation: correlation between current and lagged normalized residuals.
*
Neglected ARCH: correlation between current and lagged squared residuals.
*
Nonlinear Functional Form: correlation between the normalized residuals and
integer powers of the fitted values.
*
Heteroscedasticity: correlation between the squared normalized residuals and
the squared fitted values.
*
White's heteroscedasticity test: correlation between squared normalized
residuals and the squares and cross-products of explanatory variables.
*
Test for AR common factors: correlation between the normalized
residuals and lags of the Type 1 explanatory variables. (see para. 3 above).
*
Information Matrix Test: expected value of the difference between the
information matrix and outer product of the score.
*
Bierens' Specification Test: correlation between the normalized residuals and
a bounded nonlinear function of the exogenous variables; this test is
143
supposedly consistent against all nonlinear functional form alternatives.
Notes:
10. CM and LM tests are not available for use with the Whittle estimator.
11.
In GARCH-type models, CM tests use the normalized (variance-adjusted)
residuals as the test covariates. In tests for neglected ARCH, at least fourthorder moments must exist, and failure of this assumption can invalidate test
results - caution is advised when interpreting the findings.
12.
CM diagnostic tests are always computed with the joint covariance matrix
of scores and moments computed by the robust method (see 21. below).
Moment tests can also be specified using one of the HAC estimators,
see Actions / Compute Test Statistics / Moment Tests.
14.
It may prove impossible to evaluate the White heteroscedasticity tests
because the columns of the indicator matrix are linearly dependent.
In this case principal components of the test indicators are used, with
a corresponding reduction in the degrees of freedom of the test.
RESIDUAL-BASED TESTS
The following tests are applied to a single equation’s residuals. Hence, in multiequation models, a test statistic is computed for each equation.
*
The Durbin Watson test is included only for heritage reasons. It is
asymptotically equivalent to the Box-Pierce Q statistic for 1 lag. The LM
or CM tests for residual autocorrelation are recommended in a regression
context.
*
The CUSQ (or cusum-of-squares) test is for unconditional constancy of
the variance of the residuals in a regression model, and hence acts as a test
for parameter stability. It is computed from the absolute maximum of
the partial sums of the deviations of squared residuals from their mean,
and the location of this maximum in the sample is reported along with the
statistic, as a diagnostic aid. The asymptotically valid p-values for the test
are computed using the known analytic formula for the supremum of a
Brownian bridge, and hence are reported exactly.
*
The KPSS, RS and Harris-McCabe-Leybourne (HML) tests are
alternative tests of the hypothesis that the residuals are I(0). These are
also available for data series from the Setup / Summary Statistics dialog,
and may be useful in conjunction with the ADF and PP tests in the
context of cointegrating regression. Two parameters are selectable
to define the HML test, truncation parameter c and bandwidth
parameter L, These are selectable in the 'Special Settings' area of the
Options / General dialog. Use the default values c = 1 and L = 2/3,
or see Harris et. al (2006) for guidance.
OTHER DIAGNOSTIC TESTS
*
The Information Matrix test is an M-test that compares the inverted
information matrix with the robust covariance matrix estimator.
144
The test has k(k+1)/2 degrees of freedom when k parameters are
estimated. This can be used as a guide to correct model specification, and
can also indicate best choice of covariance matrix formula.
When least squares estimation is specified, the matrices computed are for
the concentrated Gaussian log-likelihood function. In other words, in
Gaussian ML the test is performed with the variance parameters included
in the parameter set. In Least Squares (including OLS and LGV) the
variance parameters are concentrated out, so that the test has fewer
degrees of freedom. The test is not available for 2SLS and GMM estimation.
NOTE: if the columns of the indicator matrix are linearly dependent the
statistic cannot be computed. In this case the indicators are replaced by their
independent principal components, reducing the test degrees of freedom.
*
The Nyblom-Hansen model stability test is available as a whole-model test
(degrees of freedom equal to the number of fitted parameters, including
residual variance) and, optionally, as one-degree-of-freedom tests for
individual the parameters. Check the "Individual N-H Tests." checkbox for
the latter option. These are not printed by default since the output is
potentially bulky. The tests use the table given in Hansen (1990), and the
p-values are available in inequality form.
*
The Andrews (1993) LM test of structural change with unknown change
point is available like the Nyblom-Hansen test in whole-model and
single-parameter variants. The tests use Andrews' table, with 10%, 5%
1% critical values, the p-values are available in inequality form. These tests
require an interval of the sample period to be specified (in the form of
upper and lower fractions of sample size) and the default values are pi1
= 0.15 and pi2 = 0.85. To change these settings go to Options / General /
Special Settings, and enter the values desired in the fields "Andrews Test
Lower Bound (pi1)" and "Andrews Test Upper Bound (pi2)".
*
Use the 'Coded Test' checkbox to activate/deactivate a test statistic that
has been supplied by the user as Ox code (see Appendix C). This
checkbox has the same function as the 'Test' checkbox in the Model /
Coded Function dialog. It is disabled unless code is loaded and the
'Test Only' option is selected in Model / Coded Function. In the case
where other Ox code is being compiled, this test option should be
controlled from the same dialog.
*
The bootstrap test of I(0) compares the generated values from a time
series model with i.i.d. data, to verify the validity of "short memory"
assumptions underlying asymptotic tests in finite samples. It is only
available for univariate time series models.
Note that bootstrap inference for the equation itself is disabled if this
option is selected.
CONSISTENT SPECIFICATION TESTS
Note: to simplify the interface, dialog controls for the advanced consistent tests
of functional form and dynamic specification (including Bierens tests) are not
displayed by default. To switch these features on, go to Options / General /
Special Settings, and set "Show Consistent Test Settings" to TRUE (double145
click toggle).
The consistent tests of specification, which we generically refer to as CS tests,
are based on the covariance between a target series derived from the fitted model
and an exponential test function of explanatory variables. See the main document
for full details.
*
Select the variables to appear in the test function (and a fixed number of
lags) in the dialog accessed with the Test Variables button.
To include polynomial distributed lags of the test variables (permits long
lags with fewer nuisance parameters) set the polynomial order (P) in this
dialog.
o
If P = 0 the lags in the test function are set in the Test Variables
dialog.
o
If P > 0 this setting is ignored.
*
The possible target series are
1.
model residuals (Bierens tests))
(1 d.f. test)
2.
score contributions, full gradient vector
(p d.f. test)
3.
individual score-contribution elements
(1 d.f. test).
*
The test statistics depend on nuisance parameters, and are computable in
one of three modes, depending on how the nuisance parameters are treated:
1.
Sup test
(S)
2.
Integrated test (ICM-A)
(IA)
3.
Exponential integrated test (ICM-B)
(IB)
(The right-hand column indicates how the cases are identified in the output.)
*
p-values for the tests can be computed by:
1.
"2-statistic" procedure (using standard chi-squared table)
2.
Hansen (1996) bootstrap (could be computationally burdensome).
Notes:
14. The number of Hansen bootstrap replications are set in this dialog. The
Options / Simulation and Resampling replications setting is independent of
this one. The usual bootstrap method could also be used to generate p-values.
In this case the Hansen bootstrap setting is ignored.
15.
Various test settings are found under Options / General / Special Settings;
see options with prefix "Consistent". In general, these will not need to be
changed from the defaults. They include
*
parameters for 2-statistic bound (gamma0, rho1, rho2, rho3)
*
upper and lower hypercube bounds for the weight set Ksi (Defaults
are -1, +1).
*
Precision and maximum number of evaluations for the computation
of integrated and sup statistics.
*
Maximum lag order for the polynomial lag option.
*
Scale factor for the test function, determines the range of variation of
log(w_t) over the given sample. (Default = 3, such that 0.22 < w_t <
4.48).
16.
If gamma0 is set >100 only the base statistic S_0 will be reported, with
weights ksi set to the unit vector.
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8.3 Options / Forecasting ...
FORECASTS
1.
The levels forecasts include 2-standard error bands. These are asymptotic
and do not allow for parameter uncertainty. For conditional
heteroscedasticity models, they are computed dynamically using the
volatility forecasts.
2.
The scroll bar label shows the number of forecast steps selected.
The date or observation number of the final step, which depends on the
sample selection (see Setup / Set Sample) is shown above the scroll
bar.
3.
There is no limit to the number of ex-ante forecasts. To increase the
maximum, select it, then close and re-open the dialog. However, in models
containing exogenous variables (other than the trend and GARCH_M terms)
the limit is set by the available post-sample observations.
FORECAST TYPE
4.
"Ex ante" multi-step forecasts use the lagged forecast values to projected
two or more steps forward. "Ex Post" 1-step forecasts are simply the fitted
values of the model (using actual values of all lagged and explanatory
variables) for the selected forecast period. This cannot exceed the available
observations, so the estimation sample must be set appropriately.
5.
By default, the forecast period for ex-post forecasts is set to the maximum
available observations following the 'Last Observation' set in the Setup /
Set Sample dialog. If this setting is changed, the number of forecasts is
adjusted to the default. To include fewer than the maximum number of
observations in the forecast period, change this setting after setting the
estimation sample.
6.
Ex post forecasts and forecast errors are displayed in the Actual/Fitted
and Residual plots. The main purpose of this option is to check model
stability. Two test statistics are computed, appropriate to short and long
forecast periods respectively. The chi-squared (short-period) test
(Forecast Test 1) is the generalization of Chow's (1960) second test.
and depends on the additional assumption of Gaussian disturbances under
the null hypothesis.
7.
The second test reported depends on the model. In single equation linear
regression models, Chow's stability test statistic is reported (choose
between F and Chi-squared forms by checking the box in Options /
Tests and Diagnostics.) In other cases, where the need to re-estimating
the model for sub-periods precludes generalizing the Chow procedure,
a difference-of-means test applied to the squared residuals and forecast
errors. This is asymptotically N(0,1) as both periods tend to infinity.
This is called Forecast Test 2. If it is desired to compute this statistic
for the linear regression case, simply open the Dynamic Equation dialog
and select Actions / Evaluate at Current Values.
147
MULTI_STEP FORECAST METHOD
8.
Two methods of computing forecasts and associated standard error bands
are provided. The analytic method computes formulae for the mean and
standard error of the forecast, and the plots show two-standard error bands
corresponding to 95% confidence bands when the errors are Gaussian.
9.
Two methods of computing analytic forecasts are available. New code
in version 4.38 is used by default. This method solves the model simulation
algorithm numerically, with zero shocks, and hence is available even
for nonlinear structures such as ECMs. In the case of nonlinear-in-variables
dynamics, the result is a linear approximation to the true dynamics which
may be contrasted with the stochastic simulation (Monte Carlo) method.
The new code works with most models specified through the linear
regression or dynamic specification dialogs, with the exception of Markovswitching models.
The old code, which works only for VARMA/GARCH models, is still
available by selecting this option in Options / General / Special Settings.
It is selected automatically for Markov switching models, alternatively
use the Monte Carlo method.
10.
The Monte Carlo method uses the fitted model to compute stochastic
simulations of the process, and reports quantiles of the empirical distribution
for each step. In this case all models, including those containing lagged
dependent variables as regressors, are computed by dynamic simulation.
Hence, true multi-step forecasts are reported in this case.
11.
Two types of Monte Carlo plot are available. Time plots show the median
and 2.5% and 97.5% percentiles, so that the plotted bands in this case
show a true 95% confidence interval (neglecting estimation error) even
when the disturbances are non-Gaussian. Alternatively, kernel densities can
be displayed, for the complete empirical distribution of any forecast step.
12.
Analytic standard error bands for regime switching models use a recursive
algorithm, involving m^K function calls for M regimes and K steps ahead.
In Hamilton's model, the number of effective regimes is M^(number of lags).
Unless they converge rapidly, these calculations can become very time
consuming. They are therefore terminated automatically after 100 seconds
has elapsed. Unless the bands have converged sufficiently to be extrapolated
thereafter, only the point forecasts are reported for the remaining steps.
(NB: diminishing returns set in rapidly! Even raising this factor substantially
could yield at most a couple of extra steps.)
13.
The display mode for standard error/confidence bands, including omitting
them, can be selected in Graphics Options.
14.
In dated (daily/weekly) data, it is not possible to plot forecasts with date
information beyond the end of the observed sample, since the information is
missing. An error message is displayed. In this case, either change the date
type to "No Dates", or extend the data set and supply the additional dates
manually (This must be done outside TSM).
148
MONTE CARLO SETTINGS
15.
The default number of replications is 1000.
16.
Select either the mean or the median of the Monte Carlo distribution for
reporting. In the former case, 2-standard error bands are also shown
in the plots, and in the latter case, the 2.5% and 97.5% quantiles are
shown.
17.
To select the simulation mode and change the random number seed see
Options / Simulation and Resampling.
18.
The scroll bar allows selection of one of the forecast periods for a density
plot. Note that the maximum selection varies with the setting for number
of forecasts.
ACTUALS IN FORECAST PLOT
19.
It is usually helpful in a post-sample plot to show some, but not always all,
of the series for the estimation period. The default is to include the last 50
observations. This can be changed, and to include all available observations,
simply enter any value large enough. Note that when the forecast period
includes or overlaps the data period (as for ex-post forecasts) the actual
values are always shown.
STANDARD ERRORS AND CONFIDENCE BANDS
20.
Forecast standard errors and confidence bands are enabled by default.
It may be desirable to switch them off in certain circumstances.
For example:
*
If a user-coded function contains lagged adjustment, these
dynamics cannot be taken account of in analytic variance formulae,
which will therefore be incorrect.
*
In Markov-switching models, calculation of multiple-step standard
errors can be computationally very burdensome.
*
With analytic forecasts the reported confidence bands are based
on Gaussian critical values, and should be suppressed if the
Gaussianity assumption is unwarranted.
Note that standard errors are enabled automatically with confidence bands.
21.
By default, forecasts exported to a spreadsheet file include either quantiles
or standard errors. For some purposes, particularly if further analysis is
required, it may be more convenient to export only the table of point
forecasts (e.g. median quantiles). Check the "Export Point Forecasts
Only" checkbox to enable this restricted mode of exporting.
FORECAST ERROR VARIANCE DECOMPOSITION
22.
This option is available with analytic forecasts of multi-equation models.
The values returned show, for each variable, the proportion of forecast
error variance attributable to each equation in the system. The formula
is taken from Lutkepohl (2007), page 63ff. The moving average coefficients
are computed as for analytic forecasts by solving the model numerically, and
hence are well defined even for nonlinear in parameters structures such as
149
ECMs. In the case of nonlinear models, the sequences of weights generated
provide a linear approximation to the model dynamics. The matrices of
proportions are displayed for each horizon following the standard forecast
outputs for each equation. The data are exported to a spreadsheet using
the command Files / Listings / Export Spreadsheet / Forecasts, as for
forecast outputs.
PLOT DISPLAY
23.
Ex ante forecasts can be viewed by listing values in the results window (see
Options / Output and Retrieval) or graphically (Graphics / Ex Ante
Forecasts). Check the "Display Forecasts Automatically" checkbox to
have the main graphs displayed immediately a forecast is run. Use the
Graphics menu to display plots individually, and additional items such
as Monte Carlo distribution plots.
IMPULSE RESPONSES
24.
The impulse responses (coefficients of the solved moving average process)
for levels and also conditional (ARCH/GARCH) variances, will be plotted
according to the radio button setting, in either impulse form, or step
(cumulated) form, or with both plots on the same graph.
25.
In a system of N equations, the responses shown are those on a dependent
variable of an impulse to its own shock process only (N plots). If the "System"
checkbox is checked, then the responses on each dependent variable of
impulses to each shock process are calculated (N^2 plots). This checkbox has
no effect in a single equation model.
26.
There is no limit to the number of steps possible. To increase the maximum,
select it and close-open the dialog.
27.
Only the own-shock responses can be listed in the results window. For a
listing of the full set, export the data to a listing file (see File / Listings / Save
MA Coefficients).
Note: Only the impulse responses are exported. Compute the step
responses manually by cumulation, if required.
8.4 Options / Simulation and Resampling ...
SIMULATION OPTIONS
1.
There are nine ways to generate artificial shocks to drive the one-off
simulations, Monte Carlo experiments and bootstrap tests. See the main
documentation for details and formulae.
*
'Model' uses the distribution specified by the likelihood function, if a
maximum likelihood estimator is specified. If the estimator specified
is not ML, then Gaussian shocks are used with variance equal to the
residual variance from the last estimation.
*
'Gaussian' uses normal random numbers with zero mean and the
variance specified in the text field provided.
150
*
'Stable' uses random numbers from a centred, infinite-variance
stable distribution, with the three parameters specified in the text
fields. Alpha (<= 2) is the stability parameter where 2 is the Gaussian
case, and corresponds to the largest existing absolute moment. Beta
controls skewness and 'Scale' has a role analogous to the SD.
*
'Formula' generates shocks with a user-defined formula, depending
on one or more sets of uniform and/or normal random numbers, and
optionally on variables from the data set and parameter values defined
in the model. In a multi-equation model the same formula is used with
different shocks, and parameters (if specified) specific to the equation.
Enter the formula in the dialog box provided, see section 1.5, Entering
Formulae, for details. (Note that this is "case D").
*
'Simple Bootstrap/Block Bootstrap' randomly resamples the actual
residuals, with replacement. The resampled series is centred and
multiplied by a variance correction factor, sqrt(n/n-k).
The block bootstrap is implemented by choosing a block length > 1.
*
'Stationary Block Bootstrap' is like the block bootstrap except that
the blocks have random lengths drawn from the geometric
distribution.
*
'Wild Bootstrap' preserves the heteroscedasticity of the original
sample. Instead of randomly resampling, the data are randomly
transformed by a drawing from a two-point discrete distribution.
*
The Fourier bootstrap resamples from the discrete Fourier transform
of the residuals using the Rademacher wild bootstrap, and returns
the inverse transform of the resampled series. An alternative to the
sieve-AR, suitable for Gaussian homoscedastic residuals showing
generalized autocorrelation.
*
'Data Resampling' is only appropriate for serially independent data
(cross-section data, in general). Observations (both dependent
and explanatory variables) are resampled randomly with replacement
from the specified range of the data set. Click "Set Range..." to
open the Sample Setup dialog and select the sampling range.
2.
Any bootstrap option can be combined with the sieve autoregression, in
which the resampled series are passed through an autoregressive filter fitted
to the original series. This method of accounting for sample dependence can
be combined with the simple or wild bootstraps, and also used to supplement
one of the blocking methods.
3.
Optionally (see the checkbox) the 'Model' method will always be used for
one-off simulations and Monte Carlo experiments. This setting allows the
specification of a Monte Carlo experiment where the bootstrap is used for
tests, without the need to set up different models for data generation and
estimation.
151
4.
The wild bootstrap variants are not available for Monte Carlo forecasts. If
these options are selected, the regular bootstrap is substituted.
5.
The setting 'Shock Variance' is available for Gaussian shocks only. If 0
is entered in the text field , then the sample variance from the most recent
estimation is substituted. If this value is zero (as if no estimation has been run
in the current session) then 1 is substituted.
6.
The block bootstrap option is to allow valid bootstrap inference in misspecified models with autocorrelated errors, provided the autocorrelation is
not too persistent. The chosen block length value entered in the text box is
also shown as a power of the current sample size. In the case of the
stationary block bootstrap, the mean block length is selected.
7.
When 'ML Model' is selected, the parameters of the shock distribution are
those shown in the Values / Condition Variance and Values / Distribution
dialogs. In this case the setting of 'Shock Variance' is ignored.
8.
By default the sieve-AR method used an increasing function of sample size as
maximum lag order. For this case, enter "-1" in the Max Sieve-AR Lags text
field. Setting a zero or positive value over-rides the default. Setting "0" is
equivalent to the regular bootstrap method.
9.
If 'Bootstrap/Block Bootstrap' is selected with block length 1, and the
random number seed is set to -1, the shock-generation procedure returns
the actual model residuals, in original order. The generated series should
then be identical to the original data series, apart from possible rounding
error. This feature provides a check that the simulation module is inverting
the fitted model correctly. (Note that to generate Markov-switching models
also requires a latent switching process, so this check will be valid only if
the Markov transition matrix is fixed at the identity matrix.)
10.
The option "Wild Bootstrap Skewness" sets the parameter 'a' such that the
t-th drawing is e.u_t where u_t is the sample value (fixed), and e = a and
-1/a with probabilities 1/(1+a^2) and a^2/(1+a^2) respectively. Note that
this setup preserves the first two marginal moments of the distribution.
The default is a = 1, which always yields a symmetric distribution, but
preserves kurtosis. Setting a = 1.618 preserves the original skewness
(if any) but doubles the kurtosis. The value of the Kolmogorov-Smirnov
statistic, comparing the fit of the original data points to the bootstrap
distribution, is reported to aid the best choice of this value.
SIMULATION PRESAMPLE MODE
11.
If a dynamic simulation run starts at observation 2 or later, the initial
observations can be generated in two ways, either fixed or random.
If fixed, the actual values of the selected dependent variable are used.
If random, the sequence is randomly set in each replication, using
generated or resampled shocks and the specified model. In other words,
the simulation actually initializes at date 1, whatever the nominal start
date.
152
*
If a partial sum process (unit root) is specified, the cumulation
begins at the start date, not at date 0.
*
The random presample option can be selected for Monte Carlo
experiments. Fixed (actual) values are always used for bootstrap
tests and Monte Carlo forecasts.
*
The setting makes no difference if the simulation start date is 1.
RANDOM NUMBER GENERATION
12.
The random number generator is used in several program operations,
including bootstrap estimation, Monte Carlo forecasting and Monte Carlo
experiments, as well as free-standing simulation runs initiated by the user.
It is also used in optimization algorithms based on a random search, such
as simulated annealing.
13.
The generator is initialized before running the following tasks:
14.
*
an estimation run, which may involve random optimizations,
and bootstrap-based tests.
*
a free-standing model simulation.
*
a Monte Carlo experiment, which involves both simulation
and estimation stages.
The Random Number Seed initializes the random number generator,
such that it produces an identical sequence from any given seed. If a
positive integer (an arbitrary set of decimal digits) is entered in this field,
the same sequence of random numbers will be used in successive runs,
which are accordingly exactly reproducible. If the value is set to 0
(the default) the seed is taken from the system clock (number of seconds
since midnight). Accordingly, every run will be different and not
reproducible.
INFERENCE BY RESAMPLING
15.
Two methods are implemented for generating confidence intervals and
p-values by resampling the data, rather than by asymptotic criteria.
*
The bootstrap simulates the specified model using the TSM
simulation engine with randomly drawn artificial disturbances.
These can be either drawn from a known distribution, such as
the normal or Student's t, or resampled from the empirical
distribution of the estimated residuals. Monte Carlo simulation
of the estimation procedure yields the bootstrap distribution.
*
Subsampling is the method of fitting the model to successive
contiguous subsamples of the data set, and constructing the
empirical distribution of the subsamples. It does not involve
drawing random numbers.
153
16.
The output is available in the form of confidence intervals, p-values and
plots of the empirical distributions generated.
17.
By default, resampling is deselected automatically after a single run
("Once"). There is an option to select it permanently as the inference
method ("Always"). Selection is indicated by a flag on the status line,
'(B)' for bootstrap and '(S)' for subsampling.
18.
The number of replications determines the accuracy with which the p-value
is measured. However, because of the small-sample error in the p-value
(due to replacing actual with estimated parameters) the accuracy attained
from a large number of replications is typically spurious. The default of 99
(implying accuracy is bounded by 1%) is probably adequate in many cases.
399 would be sufficient in nearly every case.
19.
The 'Static' option generates the bootstrap draws by adding the
resampled shocks to the fitted values of the estimated equation.
This procedure is equivalent to the usual bootstrap method when the
model contains only exogenous variables (fixed in repeated draws)
although it is typically much faster. On the other hand, in models
containing lagged dependent variables the resampled series are
generated conditional on the lagged actual data, not the lagged
resampled data.
20.
The 'm/T' option uses a bootstrap sample of length smaller than (a fractional
power of) the observed sample. This option may yield a consistent bootstrap
in cases of data with infinite variance. First select the number of bootstrap
replications with the scrollbar. Then, select the option and choose the
bootstrap sample size with the (re-assigned) scrollbar.
Note:
1.
The option is cancelled if the resampling method is changed to
Subsampling.
2.
The option is not available for models with exogenous variables,
21.
The bias correction option subtracts an estimate of the bias from each
parameter point estimate. This is computed as the difference between
the mean of the bootstrap distribution and the point estimate (estimating,
respectively, the mean of the estimator distribution and the true value).
22.
The fast double bootstrap is a device aimed at reducing the error in
rejection probability of bootstrap tests. It is not guaranteed to improve
performance in all cases, but showing that test outcomes are invariant to
this selection offers additional robustness.
RESAMPLING CONFIDENCE INTERVALS
23.
Resampling allows true confidence intervals for parameters to be estimated.
Three schemes for 95% confidence intervals are implemented.
Equal tails:
2.5% of probability mass in each tail, but if the
distribution is skewed, the point estimate is not
154
the mid-point of the interval.
Equal tails percentile t:
intervals based on quantiles of the distribution of
t statistics, weighted by standard errors from the
resampling distribution.
Symmetric percentile t:
intervals based on 95% quantile of the absolute
t statistics, centred on the point estimates, but
tail probabilities are unequal if the distribution
is skewed.
NEWTON-RAPHSON ALGORITHM
24.
The model is re-estimated with simulated data in each replication. For
models estimated through the Dynamic Equation dialog, this means
numerical optimization. Since the "true" values (defining the artificial DGP)
are available for starting values, the Newton-Raphson algorithm is used
for these steps. The (numerical) Hessian of the criterion is evaluated at the
true point.
25.
Numerically precise convergence is not required to reproduce the
distribution adequately. The time taken in the replications can be controlled
by both limiting the maximum number of NR iterations, or raising the
convergence criterion, or both.
26.
NR is always used for bootstrap iterations. The algorithm can optionally
be used for Monte Carlo experiments (instead of BFGS) by checking the
checkbox.
TYPE I FRACTIONAL PROCESSES
27.
A fractional (ARFIMA) model has long memory, and can depend
significantly on remote pre-sample influences. If these processes are
simulated by setting presample shocks to zero (the 'type II' model),
this changes the distribution of estimators and test statistics even in large
samples. The 'type I' model can in principle be simulated by selecting
the random presample option and setting a long presample period.
However, the number of lags required for a good approximation may
be excessive. The option 'Generate Fractional Series as Type I' (set
by default) simulates the effect of presample lags by adding a single vector
(or matrix) of Gaussian random variables with the correct covariance
structure. Selecting this option ensures that (e.g.) bootstrap distributions
match the type I case.
Notes:
1)
With this option the fractional process must be stationary, i.e.,
d < 0.5. To simulate a nonstationary process, replace d by
d - 1, and check the option "Impose Unit Root" in Model /
Dynamic Equation.
2)
The option is not available in conjunction with regime switching.
A type I process is always generated in this case.
155
3)
If the Presample data are held fixed in the simulations (required in
bootstrap and Monte Carlo forecasting) estimates or imposed
values of the presample shock components must be available.
The number of these to be included is set in the "type I Fractional"
text box in Options / General; if the setting is zero, the type II
process is generated.
8.5 Options / Graphics ...
Press the button "Line and Symbol Styles" to access a separate dialog
for controlling the appearance of series graphs. These options are
described in Section 8.5a of this manual.
TEXT ATTRIBUTES
1.
Select the font and size in points for titles, axis labels and legends in
exported files. Note that the actual appearance will depend on the
file type selected for export (see Options / Output and Retrieval.)
2.
Gnuplot graphs always use the Arial font when initially displayed. The
text style for these graphs can be changed using the context menu accessed
by clicking the top-left corner of the window.
BITMAP DIMENSIONS
3.
The dimensions of PNG and GIF bitmaps are selected by entering the
numbers of column and row pixels desired. The default is 640x480.
If 0 is entered in the column (row) field, the setting is automatically
calculated as 3/4 times the row value (4/3 times the column value).
NOTE: These settings do not affect the screen display.
DATES IN PLOTS
4.
The default date display mode is selected automatically when a new data set
is loaded. Alternative settings must then be re-selected in the dialog.
The defaults are:
*
YYYY for annual or quarterly data.
*
MM/YYYY for monthly and higher frequencies.
*
DD/MM/YY for dated (daily or weekly) data.
*
'Labels' for undated data.
5.
By default, 'Labels' are set to the row numbers of the data matrix. An option
also exists to create arbitrary observation labels as a column of the data file.
For details see 3.3, Setup/Data Transformation and Editing / Edit / Set Date
Labels.
6.
Dates are disabled in the cases of panel samples and samples selected by
indicators. In these cases, consecutive observation numbers do not in general
correspond to consecutive dates.
7.
With daily/weekday data, unless calendar dates have been loaded with the
data (see 2.2 File / Data) the date indication is generally approximate, since
there is no allowance for missing days such as holidays. In most daily data
sets with large numbers of observations, the axis labels should provide an
156
adequate approximation.
OTHER PLOTTING OPTIONS
8.
By default, plots are displayed with an embedded title. This can optionally
be either changed by the user or simply suppressed. Checking the
"Edit Title" checkbox causes a text entry box to appear when a graphic
is generated. This contains the default title, for either modification
or replacement. Note that this option cannot be selected if the "No Title"
checkbox is checked.
9.
When the origin falls in the range of the plot, the zero axis is drawn as a
light grey broken line by default. This option can be turned off using the
"Plot Zero Axis" checkbox. When the option "RH Scale" is selected in
Graphics / Show Data Graphic, two zero axes may be drawn, for the
left- and right-hand scales respectively.
10.
Plots have a white background by default. A light grey background
is a selectable option when plotting with Gnuplot 4.6.3 and later.
NOTE: This option is not available in the bundled Gnuplot 4.2!
11.
Files with extension .PLT are created by GnuDraw for processing by
GnuPlot. These are text files that can be edited for further processing
if you know the GnuPlot command language. If the box "Keep PLT
Files" is checked, these files are retained in the results folder after
creating a graphics file. Otherwise they are deleted automatically.
12.
The "Double-Chart" button on the toolbar displays, by default, time plots
of the actual and fitted values and the residuals. The button is disabled until
an estimation has been performed. If the option "Extended Actual-FittedResidual Plots" is checked, two additional plots are shown; the actualfitted scatter plot, and the histogram and kernel density of the residuals,
together with the normal density curve with matching mean and variance,
for comparison.
13.
By default, scatter plots of data include the two regression lines (X on
Y and Y on X). In the case of the actual-fitted scatter, the single line
with slope 1 is drawn (a 45 degree line when the axes match). These
lines can optionally be suppressed.
14.
A "Fill" style is used by default to highlight the display of variances and
probabilities, whose signs are always positive. This option can be
switched off by unchecking the checkbox..
CONFIDENCE BANDS
15.
By default, multi-step forecast plots show 2-standard error confidence
bands, or 95% estimated confidence bands in the case of Monte Carlo
forecasts.
The following options available for confidence band plotting.
None: also effected by turning off calculations in Options / Forecasts.
Bands: additional lines are plotted to show 95% region. The band colour
is line style 4, light green by default.
157
Bars: the default - 95% confidence region marked by vertical bars. The
bar colour is line style 4, light green by default.
Fan: bands of increasing colour intensity mark six different confidence
regions around the point forecast. The confidence levels indicated
are 98%, 95%, 90%, 80%, 60% and 40%.
Notes:
*
Fan colour is set under "Line and Symbol Styles". It
is worth experimenting with this setting since some
colours work better than others.
*
Fans are not available for monochrome plots, or
recursive forecasts. The default option (bands) is used in
these cases.
MULTIPLE SERIES DISPLAY
16.
There are three ways to plot several series at once:
*
Individual: each plot in its own frame.
*
Separate plots in the same frame (default).
*
All series in the same plot.
The last option can also be selected in the Graphics / Show Data Graphic
dialog, in which case the style of each line is selectable. Note the option
to plot the last selected series against the right-hand axis in this case.
17.
If a system is estimated, the above three options are available for plotting
the series associated with each equation: actuals, fitteds, residuals etc. If
the "Individual" option is selected, only the series for the equation
selected in the "Equation" choice widget on the tool bar is plotted.
LEGENDS
18.
Legends are used to label series when two or more appear in the same
frame; otherwise, the series name appears as the plot title. There are five
options for placing the legend in the frame:
X
No legend.
TL
Top left corner (default)
TR
Top right corner
BL
Bottom left corner
BR
Bottom right corner
Note that these are general settings. It is not possible to place the legend
differently in different plots in the same frame.
19.
Check the "Box" checkbox to enclose the legend in a box. By default,
no box is shown.
3-D PLOTS
20.
There are three options for the three-dimensional plots created by Actions
/ Plot Criterion Grid and Graphics / Show Data Graphic / Bivariate Density.
If "both" is selected, the resulting plot is the same as the surface plot with
contours drawn on the 'floor' (p_1, p_2 plane) of the three-dimensional
graph.
158
DISTRIBUTION PLOTS
21.
These plots are available to for univariate and bivariate data distributions,
bootstrap and subsampling distributions and Monte Carlo distributions,
and also for Monte Carlo ex ante forecast distributions at specific dates.
Optionally, either or both of the kernel density estimate and the histogram
can be selected, with both selected by default. Also optionally available are
the normal curve with matching mean and variance and, for univariate
distributions only, the cumulative distribution function (CDF) plotted in a
companion frame.
8.5a Options / Graphics / Lines and Symbols
Series can be plotted by lines connecting the data points (default), by symbols
at the points, or by both lines and symbols.
Plots can be selected as colour or monochrome where in the latter case, full
lines and patterns of dots and dashed lines can be selected.
These are general settings. The choice of individual colours and styles for each
line is selected in the line and symbol styles area.
Notes:
1.
If the "Lines" radio button is selected, the Symbol choice widget and
size selector are disabled.
2.
If "Both" is selected, the inclusion of symbols can be overridden for
individual lines by choosing "None" in the Symbol choice widget.
3.
In Microsoft Windows, line widths and patterns can be further edited
by clicking by clicking the top left corner of the Gnuplot display
window and choosing Options / Line Styles... from the menu.
LINE AND SYMBOL STYLES
Eight line styles for series plotting can be set by the user.
The selectable option are line colour (or pattern, for monochrome plots), line
width, symbol type, and symbol size.
First select the line to be styled with the radio buttons. Then select options
with the line and symbol choice widgets, and line width and symbol size fields.
*
Available line widths are 1 (thinnest, default) to 6 (thickest).
*
Symbol size can have any positive value, 1 is default.
*
Monochrome lines can take any width, if solid.
*
Patterned lines (dots, dashes, etc.) are always of thickness 1.
Press the 'Restore Defaults' button to set all line settings to defaults.
Notes:
4.
The Colour/Pattern widget shows different options, depending on whether
the colour or monochrome plots option is selected. Note that both settings
(colour and pattern) are remembered. Switching between colour and
monochrome plots does not delete the options.
5.
The eight line styles are used for data series plotting in the
multi-series plot option in Graphics / Show Data Graphic.
159
6.
If a multi-series graph is plotted by selecting 'One Graph' under Multiple
Series Display in the Options / Graphics dialog, the line styles are used in
order, starting with 1.
7.
Equation graphics are drawn using line styles 1-4.
*
Style 1 is used for the main series in each plot, including the 'Actual'
series in Actual/Fitted plots.
*
Style 2 is used for 'Fitted' series.
*
Style 3 is used for forecasts.
*
Style 4 is used for confidence bands.
8.
If multiple equation series are plotted in a single graph, the line styles are
incremented by two, or three, so as to cycle through the available styles.
9.
The symbol option 'Fill' does not draw a symbol, but shades the region
between the line and the zero axis using either light gray in colour plots,
or a hatching pattern in monochrome plots.
Optionally, this style is used by default in the display of probability and
conditional variance series. This option is enabled by default, uncheck
the checkbox in the Options / Graphics dialog to use Line Style 1 for
these series.
10.
The "Band Fill" line style is a special option to indicate regimes or time
periods, depending on the value of the selected variable. It displays light
grey bands in those periods when the variable is positive.
NOTE: Band Fill can only be selected for Line 8. Attempting to select
it for Lines 1-7 produces a warning message.
11.
The "Fan" style is to select the colour to be used for fan charts. Note
that the series itself is drawn in a contrasting colour, and the results are
not always predictable from the description. Experimentation is
recommended!
SCATTER_PLOT OPTIONS
12.
Scatter plots styles allow the form, colour and size of symbols to be
chosen. Scatter 1 is used for all data plots, and for actual-fitted plots.
Scatter 2 is used only for the post-sample actual-forecast scatter
when the one-step forecasting option is selected.
13.
The "RGB Scatter" option colour-codes the points in a scatter plot
according to their position in the sample. The initial points are coloured
red, those in the middle green, and the end of the sample blue, with
a smooth interpolation from one colour to the next. Try plotting the
scatter of a variable against the trend dummy to see the effect. Select
a 'filled' symbol (square, circle or triangle) for best results. If
monochrome plots are selected, the coding is a greyscale, running from
black to white.
Note: This option is not available for actual-fitted plots which include
post-sample actual-forecast points.
160
8.6 Options / ML and Dynamics ...
ML PARAMETERIZATION
1.
The residual variance and GARCH intercept are scale-dependent
parameters, bounded below by zero. In some models, such as highly
persistent FIGARCH models, the GARCH intercept can be very small
and estimation close to the parameter boundary poses numerical problems.
These are eased by making the square root (or other fractional power) the
parameter to be estimated. The default value, which works well in most
cases, is 2. Try raising this to 4 if there is evidence of a problem. Set to
1 to estimate the variance/intercept directly. Be careful to set the starting
value and interpret the estimate appropriately.
2.
The Student's t degrees of freedom (d.f.) parameter is bounded below by 2,
and is infinite in the Gaussian case. A square root transformation (the default)
better numerical performance in the vicinity of these can yield extreme
values. Setting the order of root to a negative value allows the estimation
of the inverse d.f., which takes the value zero in the Gaussian case.
3.
Note: the variance/GARCH intercept and Student t d.f. parameters are
constrained to be nonnegative during optimization by taking the absolute
value of the parameter element to evaluate the likelihood function.
4.
By default, the Student skewness parameter is non-negative and equal to1
in the symmetric case. Estimating the logarithm makes 0 the symmetry value,
and may yield better numerical properties. (In the default case, non-negativity
is enforced as in 3.)
DYNAMIC MODEL SETTINGS
5.
By default, up to 10 lags can be set in the ARMA and GARCH models.
This maximum can be reset to any desired value in the text box.
6.
There is no accepted convention regarding the signs of the coefficients
of a moving average lag polynomial. The program default is to report
the MA coefficients theta_j in
theta(L) = 1 - theta_1 L - ... - theta_q L^q,
and GARCH coefficients as beta_j in
beta(L) = 1 - beta_1 L - ... - beta_r L^r .
This is consistent with the convention in equation (4.8) of the main
document, and also more natural. For example, in the ARMA(1,1)
model equal roots cancel each other out, and in this case the estimates
will be equal. Similarly, in the ARMA-in-squares representation of the
GARCH(1,1) model, beta_1 = delta_1 corresponds to alpha_1
= 0, and the estimates are again equal in this case. However, the
MA coefficients can be optionally reported as theta_j in
theta(L) = 1 + theta_1 L + ... + theta_q L^q,
and GARCH coefficients as beta_j in
beta(L) = 1 + beta_1 L + ... + beta_r L^r.
7.
If the first observation for estimation is greater than 1, lag distributions
will normally be computed using all available pre-sample lags.
161
Checking 'Restrict Pre-Sample Lags' allows the number of presample
lags to be set in the textbox provided. Thus, setting 'Lag Truncation'
to 0 means that all pre-sample values are replaced by 0. This provides
comparability with the situation when the first observation used for
estimation is 1.
8.
The roots of dynamic systems (autoregressive and moving average lag
polynomials, also the GARCH model counterparts of these) are
computed by default. In very large models, in particular large BEKK
models, the algorithm to compute the roots can become unduly time
consuming. These calculations can be optionally disabled by unchecking
'Compute Roots'.
9.
For details of the option "Type I Fractional" see 4.2 Model / Dynamic
Equation, and Davidson and Hashimzade (2009).
10.
In systems of equations featuring fractional differencing and/or a
nonlinear ECM, checking the checkbox "Difference Spec'n for System
FI & ECM Parameters" causes the equations to be parameterized so
that equation 1 is the reference case, and the parameters in the other
equations are measured as differences from this case. This option makes
it easy to test and/or impose the restriction that the parameters are equal
across equations.
Note: This control is duplicated in the dialog Model / Equilibrium
Relations.
GARCH PARAMETERIZATION
11.
As the default, GARCH coefficients are reported in 'ARMA-in-squares'
form, in which delta(L) and beta(L) in equations (6.1) and (6.2) are the
AR and MA components. In this case the coefficients are named
"GARCH AR1", "GARCH MA1" etc., etc. Optionally they can be
reported in 'standard' form, corresponding to the representation of
Bollerslev (1986). In this case, the coefficients named "GARCH Alpha1"
etc. are the coefficients of beta(L) - delta(L), and "GARCH Beta1" etc.
denote the coefficients of beta(L).
Note:
*
Roots of the GARCH AR polynomial are not reported when this
option is checked.
*
The EGARCH model does not strictly have an “ARMA-insquares” representation. The default corresponds the stated
form of equation (6.2). The 'Bollerslev' form is the one more
commonly reported.
*
It is the user's responsibility to match starting values to the
convention selected.
12.
The GARCH intercept can also be computed in two different ways. By
default, it is 'omega' in equations (6.1) and (6.2). By unchecking the box
"Specify 'Type 1' GARCH Intercept", kappa = omega*beta(1) will be
computed instead, see equations (6.4)ff of main document.
162
OPTIMIZATION SETTINGS
The following options should not normally need changing, but the defaults may not
suit all cases. Experimentation is recommended if in doubt.
13.
The GARCH-M likelihood is computed by Gauss-Seidel iteration of
equations (4.1) and (6.1), (or (4.1) and (6.2) for EGARCH). A fixed number
of iterations is used, the default is 5. Increasing the number will increase
computation time, but may not improve the estimates significantly.
14.
To stabilize the GARCH-M calculations, h_t (or h_t^{1/2}) is trimmed
before inclusion in equation (4.1). The upper bound is set to a multiple of
the sample variance (or standard deviation) of the data, called the trimming
factor. Try reducing this setting in case of failure of the algorithm.
15.
The EGARCH likelihood can be computed in one of two ways; direct
nonlinear recursion of equation (6.2) (default) and Gauss-Seidel iteration;
i.e., repeatedly solving the linear difference equation obtained by
conditioning on h_t^{1/2} in equation (6.2). There may be small differences
between the two estimates due to treatment of initial conditions. The
main consideration in this choice is one of speed. The nonlinear
equation cannot be solved using Ox's vector manipulation capability,
and has to be programmed as a loop. This could result in long solution
times in large samples, and the iterative method will often be quicker.
A convergence criterion is used to control the G-S iterations. The
default maximum number (50) should not need changing.
8.7 Options / Optimization and Run ...
OPTIMIZATION SETTINGS: BROYDEN-FLETCHERGOLDFARB-SHANNO (BFGS) ALGORITHM
1.
The options Maximum Number of Iterations, Iterations Print Frequency,
Strong Convergence Criterion and Weak Convergence Criterion are set
to their Ox defaults with the value -1. They will not normally need to be
changed.
2.
Printing of the current position and gradient is performed every N iterations,
where N is the print frequency. This output is under the control of the Ox
routine, and will not appear in the TSM results window. It goes only to
'standard output', meaning either the console window or OxEdit/GiveWin
output, depending on operating mode. Set frequency to 0 for no printing.
3.
Due to rounding error, the efficiency of the search algorithm can be
sensitive to large differences in scale between parameters. This can be due
to inappropriate units of measurement, for example. Setting the Parameter
Rescaling Factor to 1 adjusts parameters to have a similar order of magnitude,
based on the starting values - hence this setting alone will not have any effect
with default starting values. However, setting to a value greater than 1 scales
all parameters up, to limit rounding error. The value of 10 appears to improve
the performance of the algorithm in at least some cases. However, no
verified guidelines can be offered. Experiment! (and report your findings,
please.) To disable rescaling (the default) set the factor to 0.
163
4.
Check the "Use Numerical Derivatives" checkbox to force the use of
numerical derivatives. TSM uses analytic derivatives by default to compute
the BFGS step, when these are available. Some of these routines are is still
under development. In the event of a convergence failure, TSM compares
analytic and numerical derivatives and switches to the latter automatically if a
discrepancy is found. This option is saved as part of the model's specification.
Note that analytic derivatives are not implemented for some models.
SIMULATED ANNEALING
5.
Optionally, a simulated annealing algorithm can be run for a fixed number
of iterations to provide starting values for BFGS. This option is selected
by default. By choosing a large number of iterations, SA can be effectively
made to act as the search algorithm proper. However, given good starting
values BFGS should be much faster, so a compromise is probably best.
6.
The other three settable SA parameters are the initial temperature, the
temperature reduction factor, and the number of iterations before
temperature reduction. None of the defaults are necessarily best. If the
number of iterations before temperature reduction is set <= 1 it is replaced
by the default of max(100, 5*(#parameters)). This setting appears as
.NaN in the text field.
OPTIMAND CONVENTION
7.
Two of the estimators available (least squares and GMM) are
conventionally regarded as minimizing a criterion, while the ML options
are maximands. This can lead to confusion, especially when interpreting
the model selection criteria. The "optimand" for least squares and LGV
is reported for comparability as the Gaussian log-likelihood (a monotonedecreasing transformation of the sum of squares) but the GMM optimand
has no such counterpart. By default, all the estimation criteria are treated
as maximands, (so, -GMM criterion). The 'Report Minimand' option
reverses the signs (so, -Log Likelihood). The important issue is that the
selection criteria are always signed in the same way as the estimation
criterion, and so are to be minimized (maximized) if this option is checked
(unchecked).
NUMBER OF GRID POINTS
8.
Enter an integer value here to choose the density of points computed in
a grid plot. If N is set, then N+1 points are evaluated in a 1-dimensional
grid, or (N+1)^2. points in a 2-dimensional grid. Note that grid plotting
must be enabled in Values / Equation, and the run launched with Actions
/ Plot Criterion Grid. Set the grid bounds(s) in the relevant Values
dialog(s).
SUPPRESSING THE OUTPUT
9.
Optionally, computation of estimation outputs including residuals,
covariance matrix, test statistics and forecasts can be skipped. This
option may be useful in big models where these calculations are timeconsuming, and the user is performing a sequence of restricted
164
optimizations. (This can be a good strategy for optimizing poorly
conditioned criterion functions.) The best parameter values attained are
stored and can be inspected in Values. The full outputs can then be
computed using the "Evaluate at Current Values" command, if required.
Likewise, if the search algorithm fails to converge or is interrupted by
the user, the output at the attained point can be evaluated in the same
manner.
RUNNING AN EXTERNAL PROCESS
10.
The option of running estimations as independent processes from the
command line allows the TSM GUI to remain under the user's control
for other tasks while a long numerical optimization is performed.
It also allows two or more jobs to run be concurrently. Since Ox is
not multi-threaded, this is the best way to make full use of a multi-core
processor.
11.
If the option "Run Next Estimation as External Process" is checked
before launching an estimation run, the calculations are run in a new
instance of Ox, running in a console window. A temporary executable
Ox file is created to be run in batch mode. The usual estimation results
are written to a text file identified by the run number. Import this text
to the results window using the command File / Load Text File.
12.
The option is cancelled once the run is executed. Reset it in this
dialog as required.
13.
If the specifications are stored as a named model in Model Manager
before running the new process, the associated values and listings
can also be imported. A ".tsd" data file is created with the usual
outputs. Import the data by RE-loading the model in Model Manager.
Also, the estimates can be loaded for further processing by the
command Restart / Load Text Input. The name and path of the file
to load is given in the results window.
14.
If the option "Delete Temporary Files on Exit" is checked, the
temporary code and listing files created by this option are deleted
at closedown. Results files are not removed, and must be deleted by
hand, as required.
RUNNING A CONDOR JOB
15.
On a network equipped with the Condor HTC system, estimations
can also be run on otherwise idle machines attached to the network,
and the results returned to the TSM work-station, "as if" run as local
external processes. See Appendix H for more details on the use of
Condor.
8.8 Options / General Options ...
INTERFACE SETTINGS
1.
Dialogs are closed when an estimation run is started. Checking the option
"Restore Dialogs Automatically" causes them to re-open in the same
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positions at the end of the run. Dialog positions are stored in “settings
.tsm”, so the last configuration in the previous session will also be restored
at start-up. If this option is not selected, dialogs can be restored manually
using the Actions / Restore Dialogs command.
2.
The positions of dialogs on the screen are remembered during a session, but
by default are lost when the program is closed. They are positioned centrally
when first opened. Optionally, the program will remember the positions
between sessions. This allows the user to maintain a preferred screen layout,
but note that if the monitor resolution is changed, they could become invisible.
In this event, use the command Actions / Reset Dialog Positions to re-centre
them.
3.
By default, the user is prompted to save data/results before over-writing
them or closing the program. Deselecting "Enable Saving Prompts"
suppresses these reminders.
Note: The prompt to clear model specifications when loading a data set can
be optionally skipped (select "Always"). The prompt is re-activated by
deselecting and then reselecting this option.
4.
"Automatically Close Options Dialogs" is selected by default, and has the
effect of closing any options dialog currently open when another is
opened. This saves a proliferation of open dialogs on the screen, but
can be disabled if it is desired to work on two or more options dialogs
at once.
5.
TSM output can be echoed to the console as well as appearing
in the results window. To enable this behaviour check the "Echo
Results to Console" box. Output from Ox not under the control of
TSM, such as error messages, will also to appear in the console
window.
6.
Drag selection allows the quick highlighting of a block of adjacent variables
in any list allowing multiple selection. Select a variable as usual, then put the
mouse pointer on another variable, and "drag" briefly (hold down the mouse
button while moving the mouse). These actions select all the names in
between. De-selection works the same way. The option can be switched off
in case it fails to operate smoothly on particular systems.
7.
Tool tips appear by default when the mouse pointer is passed over the
tool buttons. These can be optionally switched off.
8.
The default font size of 12 points should suit most monitors, but can be
changed. This setting also effects the help pages, whose widths are
increased to accommodate the larger text. The results window is
resizable by dragging the corner with the mouse.
9.
The results window background can be either white or tinted, to make
the TSM window easier to locate on a crowded desktop, or simply easier
on the eye. The button cycles through five preset choices (white, red,
green, blue, gray) and a user-selectable color. The latter (yellow by
166
default) is set by editing the file tsmgui4.h and changing the RGB values
in the function "Get_TextAreaBG()".
OPERATIONAL SETTINGS
10.
Saving model settings in Model Manager can always be done manually
but the option "Save Model After a Run" saves model settings and results
automatically after each run. Enabling this option allows an earlier estimation
run to be re-created instantly, by re-loading the model.
NOTE: A maximum of 100 models can be stored at once. Use this setting
sparingly to avoid a cluttered results folder!
11.
The current results (estimation output, graphs, series, Monte Carlo
results etc.) can be saved in the settings file at closedown, along with the
settings and model specifications. This means that the last estimation results
can be redisplayed without having to be recomputed. (Click the
"Evaluation" button, then "Yes"). The program is in almost exactly the same
state as at the last closedown, but the complete contents of the results
window are not stored. Save these in the usual manner.
12.
Enabling the option "Delete Temporary Files on Exit" will cause .TSD
(model results and data) files to be deleted automatically at the end of a
session. Uncheck this if you wish to keep your model results, or check
it to avoid excessive clutter in your results folder.
13.
Data descriptions are saved as extensions to the series names, following
a delimiter character (@ by default). These extended names may not be
compatible with other programs. Set the option "Omit Data Descriptions"
when exporting data for use in other packages.
14.
The Files / Settings / Export command saves a complete image of the
current session, including data, for export to another installation. If
user-supplied Ox code is loaded, this can optionally be bundled in the
export file. Then, loading the settings re-creates the files needed to run
the supplied code at the target installation.
15.
If the Enable Error Recovery option is checked (the default) the program
restarts automatically in the event of a crash (Ox error). Note that the
Ox error message appears in the DOS console in this case.
LINEAR REGRESSION MODE
16.
To simplify the user interface for teaching purposes, the options for
nonlinear estimation by numerical methods can be disabled, and the toolbar
buttons hidden. For this option, uncheck "Enable Optimization Estimators".
A restart is required to implement this selection.
DEFER EXTERNAL JOBS
17.
Check this option to create batch jobs (estimations or Monte Carlo jobs)
as executable Ox files, for starting manually. Use this option to run the job
on a different Ox installation, or to defer running it until a convenient time.
When this option is unchecked (the default) the job is started immediately
the Run command is given.
167
LOAD MULTIPLE DATA SETS
18.
By default, multiple data sets can be loaded simultaneously. Data are
reloaded at start-up and are not removed from memory except by
executing one of the Clear commands under Setup / Datasets. This feature
can optionally be disabled, so as to limit the amount of memory used by an
instance of TSM, or just to simplify the operation of the program.
A restart is required to implement this selection.
ASSIGNABLE TOOLBAR BUTTONS
19.
Up to 6 toolbar buttons, showing the "Dialog" icon and a number, can be
assigned to run any command and open any dialog that does not itself have
a dedicated button. To assign a button, first run the menu item you wish to
assign. Use the pull-down menu to select a button for assignment, and then
click "Assign to last Dialog Opened". The new button appears on the
toolbar. To remove the assignment, click "Clear".
Note:
o
To assign an Options dialog to a toolbar button, first deselect
"Automatically Close Options Dialogs" under Interface Settings.
This allows both Options / General and the other dialog to be
open together.
o
With Tool Tips activated, view the current assignment by
hovering the mouse pointer over the button.
o
Buttons 2-6 are removed from the toolbar if unassigned.
Button 1 is set to the default of re-opening the last dialog
opened.
SPECIAL SETTINGS
20.
A pull-down menu gives convenient access to a range of parameters that
control the performance of various tests and other procedures selectable in
the program. These are gathered here to reduce the clutter in other options
dialogs, since they are changed only infrequently. This facility is designed
to be expandable as more tests and diagnostic procedures are added to
the program in the future.
21.
If a parameter take a fixed number of discrete values, such as "TRUE" and
"FALSE", simply double-click the text box to change the setting, or cycle
through available values when there are more than 2. Otherwise, type
numerical values into the text box. Passing the mouse pointer over the box
registers the new value. Be careful not to move the mouse while typing
the entry.
22.
In "Initialize Run ID", enter a nonnegative numerical value to reset the run
counter to that value. The change comes into effect the next time
"settings.tsm" is saved (e.g., the next time an estimation is run). The entry
displayed then reverts to the default value, "OFF". If the next action
following this one is to give the command File / Settings / Export..., the run
counter is set to that value in the exported settings, but the current counter
is left unchanged. (By default, the counter is set to 0 in an exported file.)
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23.
Other special settings are in some cases explained in their context. The
following are settings not documented elsewhere:
"Show CS Test Settings"
If set to TRUE, settings for the suite of consistent specification tests
(including the Bierens test) are shown, here and also in the Options /
Tests and Diagnostics / Diagnostic Tests dialog. By default these items
are hidden to simplify the interface.
"Use HAC Covariance Matrix in Tests"
A number of test statistics, especially the tests of weak dependence,
depend on HAC estimates of the covariance matrix of scores or
residuals. HAC is also an optional choice for the calculation of standard
errors and test statistics via the residual covariance matrix. This option,
set to TRUE by default, makes the choice for these additional tests
independent of the selection in Options / Tests and Diagnostics. HAC
will be used regardless of the dialog setting. Set this option to FALSE to
make all selections subject to the dialog setting.
"Chi-Squared Probit"
Use the chi-squared distribution to define the probit latent variable, with the
degrees of freedom an additional parameter.
"Automatic Data Transformation"
Enable the option to let data series be transformed for inclusion in a model.
(See 4.0 for details.)
"Annual Difference Forecasts"
Forecasts are reported as the percentage change from the observed data
in the previous year (4 quarters or 12 months back). In this case, a
maximum of 4-quarters or 12-month forecasts can be computed.
"Plot with GnuPlot 4.2 (restart)"
If the full Gnuplot package (version 4.6.3 or later) is installed, it will be
used to create graphics in place of the compact bundled version, Gnuplot
4.2.6. Setting this option to TRUE forces TSM to use the bundled version
even if later versions are present. This option must be set before showing
a graphic, or else a restart is needed for the change to take effect.
NOTE: If this option is set to FALSE, the installed Gnuplot version MUST
be v4.6.3 or later, or else plotting will not work!
"Censor MC Replications"
In Monte Carlo experiments, a function coded by the user in Ox can be
used to examine the result of a replication and optionally discard it, for
example, because parameter estimates take illegal values or otherwise
represent a false maximum of the estimation criterion. See Appendix C
for details.
"Tabulate p-Values in EDFs"
In bootstrap inference the computed p-value is for some purposes a
natural test statistic, having a uniform distribution asymptotically under
169
the null hypothesis. In Monte Carlo experiments on bootstrap tests,
this option tabulates the p-values instead of the test statistics.
"Show Stubs"
When this option is set to TRUE, the function prstub(), included in a
user's Ox function, writes its arguments to standard output, with
spaces automatically inserted between the printed items. This is a
code development tool. Use it to check on intermediate outputs
and diagnose crashes.
Note: this setting is not stored. It must be set each time TSM is started.
"Omit Mean of EGARCH Abs. Shocks".
This is a backwards compatibility option, suspending the change made
to the EGARCH model specification in release 4.32.08-06-14. The
theoretical mean of the absolute normalized shock is replaced by zero in
the definition of the EGARCH volatility indicator.
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9. Help
*
"User's Manual" gives access to these pages.
*
"View Text Files" opens additional documentation in ASCII files, for
reading only.
*
"Data Descriptions" opens a list of names of the currently loaded
variables, followed by any description that has been created for
the variable. The description is preceded by the symbol @.
*
"Register this Copy..." opens a dialog to enter the user's name and
the unlocking key provided to registered users of the software.
*
"About" opens a box showing copyright information and the registered
username.
USER'S MANUAL
1.
Navigate the User's Manual by the menu (sections) and sub-menus
(subsections), and also by clicking the "Previous" and "Next buttons to
move backwards and forwards through the pages. These pages
duplicate the contents of the PDF file "tsmod4ghp.pdf", which is
accessible through the Start Menu (Windows).
VIEW TEXT FILES
2.
"File Dialog" opens the file dialog, to select any ASCII file for reading.
3.
"Most Recently Opened" repeats the last selection. By default (if
no file has yet been opened) it opens "notes.txt" if this file exists.
4.
'Imported Ox Code' refers to a source code file, with .ox extension,
which has been loaded from a distributed settings (.tsm) file. A
distributor of coded functions has this opportunity to document their
code, by including text comments in the file before the code
statements. The code itself can also be inspected.
DESCRIPTIONS
5.
Data descriptions can be created in two ways. In Setup / Data Editing
and Transformations, the choice widget item "Description" opens a text
field where the description of the selected variable(s) can be entered.
Alternatively, when the data are prepared for loading in a spreadsheet
or text editor, add the description text to the variable name, normally
preceded by a @ symbol. The delimiter symbol can be changed by
editing the tsmgui4.h file.
6.
Some entry formats, such as .DAT, limit the length of a variable name.
Overflowing text will be lost if the data are saved in this format.
7.
"Show Settings Info." displays the header from most recenty opened
settings file (with .tsm extension). This contains the TSM version used
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to create the file, the data and time of creation, and whether the
settings were Exported (created with the File / Settings / Export...
command and hence portable between installations.
REGISTRATION
8.
The username must be entered in exactly the format as given with the
unlocking key. Changes in (e.g.) spelling, capitalization, embedded
spaces, etc., will cause the registration to fail.
9.
The program saves the licence file "registration.txt" in one of the two valid
locations for this file. It first tries the TSM Home directory, i.e., [ox home]
/packages/tsmod4/. If either the user does not have permission to write in
this folder, or if a licence file already exists there, it writes to the current
Results folder. This allows several different licences to coexist on the same
workstation, if each user maintains a different Results folder.
10.
By default, the Results folder is the "start-in" folder specified in the short-cut
used to start the program. However this location can be changed (e.g. by
the command "File / Results / Locate Results Folder"), and new location is
saved in "settings.tsm". If the settings file is subsequently deleted, it will be
necessary to either restore the Results location, or move the licence file
manually to the new one
11.
TSM reads the licence file at start-up, and looks for it in the current Results
folder first. If it is not found there, the program looks in the TSM Home
directory. If a licence file exists in the current Results folder it will 'take
precedence', and any licence file stored in the TSM Home directory will be
ignored. To "see" the latter registration, change the Results folder.
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10. Interpreting the Output
PARAMETER LABELLING
1.
The symbols AR1, AR2, ..., MA1, MA2,... are used to label the ARMA
coefficients in the output. The prefixes 'GARCH', 'EGARCH' or
'APARCH', as appropriate, are appended for the conditional variance
coefficients in the default case of the 'ARMA-in squares'
parameterization. For the standard (Bollerslev) parameterization, 'AR'
and 'MA' are replaced by 'Alpha' and 'Beta', respectively. These
notations are also used for the BEKK multivariate GARCH model. Be
careful to interpret the latter parameters correctly!
2.
For models specified in the Model / Dynamic Equation dialog, the 'Type'
of a regressor appears as a prefix in square brackets, for example,
"[1]Var1" denotes that Var1 is a regressor of Type 1. This prefix is
omitted if only Type 1 regressors are specified, and also in equations
specified in the Model / Linear Regression dialog.
Note: in the latter case the Type only controls the number of lags
generated, not the interpretation of the coefficients.
3.
A GARCH regressor is indicated similarly, with an additional "G" prefix.
For example, "[G1]Var1" denotes that Var1 is a GARCH regressor
of Type 1. The GARCH (or EGARCH or APARCH) intercept of
Type 2 ('kappa') is indicated with the prefix '[2]'. However, no indicator
is used for the GARCH (EGARCH, APARCH) intercept of Type 1
('omega').
4.
To indicate the regime in an explained regime-switching model, the
regressor has an additional "Rg" prefix. For example, "[Rg1]Var1"
denotes that Var1 is a regressor explaining the probability of switching
to Regime 1.
5.
In smooth transition models, the parameters of the single and double
transition factors are indicated with the prefix "Sm". For example,
"[Sm1]Intercept" denotes the location parameter of the first transition
factor.
6.
The bilinear model is described in the output as 'BilinearAR(F)IMA(p,r,d,q) where r refers to the selected bilinear order, and
p, d and q are as for the standard AR(F)IMA model.
PARAMETER ROOT TRANSFORMATIONS
7.
By default, the GARCH intercept term is estimated in square root form.
Correspondingly, in ML estimation of models without a conditional variance
component, the error standard deviation is estimated by default. This is
for reasons of numerical stability. Particularly in IGARCH models where
the parameter can be close to zero, numerical derivatives can be highly
inaccurate without a rescaling transformation. The transformation can be
selected by the user in the Options / ML and Dynamics dialog. In certain
cases, raising the order of root from 2 to 4 may be found to aid
173
convergence, while in others 1 will work satisfactorily
8.
Similarly, the parameter of the Student t distribution can optionally be
estimated as a root of the degrees of freedom. The square root is the
default. See the Options / ML and Dynamics dialog to set alternative
values. This is again for reasons of numerical stability. The parameter
is both bounded below, and infinite in the Gaussian case, and extreme
values are potentially difficult for numerical differentiation. By setting the
root to a negative value, the inverse transformation can be applied, such
that the parameter is zero in the Gaussian case.
STANDARD ERRORS, TEST STATISTICS AND P-VALUES
9.
Every estimated parameter is shown in the output with either its
estimated standard error , or the words "Fixed" or "Solved" when the
parameters have been so designated in the Values dialogs. Following
the standard error, most parameters show the t ratio and nominal
p-value of the significance test. The degrees of freedom are calculated
as "sample size - (total model parameters)/(number of equations)".
10.
Parameters for which there is no natural "zero hypothesis" to be tested,
such as the variance, GARCH intercept, Student's t degrees of freedom,
etc., are shown with standard error in parentheses but no p-value.
11.
Nominal p-values are also given for quoted test statistics, in many cases
asymptotic chi-squared statistics. For tests with non-standard
distributions (Dickey-Fuller, KPSS, R/S) these are computed from the
available tables. Since the coverage is incomplete, these results are shown
as inequalities. Thus, {<0.05} would denote that the p-value is less than
0.05 (leading to rejection at the 5% level) according to the table. The result
{<1} simply indicates that the statistic falls within the bounds of all the
tabulated points. The tables themselves are given as an appendix to the
main document.
12.
If standard errors and/or test statistics print as NaN, (stands for "not a
number") this means the Hessian matrix of the optimization criterion could
not be inverted at the current point. Typically, this means the local optimum
is not unique, which will also cause convergence failure. Lack of
identification is a leading cause; for example, a Markov switching model
with a zero-probability regime. When Print Covariance Matrix is selected
in Options / Output and Retrieval Options, the Hessian matrix itself is printed
in this case, as a diagnostic aid. Checking for zero rows and columns could
indicate the source of the problem.
SELECTION CRITERIA AND SUMMARY STATISTICS
13.
By default the model selection criteria (Schwarz, Hannan-Quinn and Akaike)
are defined as "maximand less penalty". Therefore, larger values are preferred.
This convention can be optionally reversed, see "Report Minimand" in
Options / Optimization and Run.
14.
"R-Squared" is the squared correlation coefficient between the dependent
variable Y, and the model predictions ( = actual Y - residuals). Therefore,
174
it is well-defined for any model, and must lie in [0,1]. However, whether it
is a useful measure of model performance depends on the model - it is of
no use in assessing GARCH models, for example.
15.
"R-Bar-Squared" is calculated as 1 - (1 - R-squared)*(T-1)/(T-p) where
p is the number of parameters fitted in the model.
16.
When models are estimated by Instrumental Variables from the Linear
Regression menu, the Sargan and DWH (Durbin-Wu-Hausman)
statistics are given. These are asymptotic chi-squared statistics under
H0, with degrees of freedom indicated, and nominal p-values shown in
braces. The Sargan statistic is N times the ratio of the GMM minimand
to the residual sum of squares, where N is sample size. This tests validity
of over-identifying restrictions. The DWH statistic tests for exogeneity
of the regressors and is N*(RSS0 - RSS1)/RSS1 where RSS0 is the sum
of squares from the OLS regression, and RSS1 the sum of squares from the
regression including the reduced form residuals for the included endogenous
variables.
CONVERGENCE ISSUES
17.
All estimations specified in the Model / Dynamic Equation dialog are
done numerically. The optimization routine is the Ox implementation of the
Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton procedure. This
method reports strong convergence in a high proportion of cases. However,
don't assume that the message "Strong convergence" means that the
estimation criterion has been globally optimized. It simply means that a local
optimum has been found. Restarting the search algorithm from different
points is the only way to confirm a global optimum.
18.
The messages "Weak convergence" or "No convergence" may also be
returned by the search algorithm. A run may also terminate with the
message "Estimation failed! Algorithm returns NaN or +/- infinity". This
typically indicates overflows in the floating-point calculations, e.g.
dividing by zero or attempting to take the logarithm of a negative number,
probably due to inappropriate starting values. There is an option to have
optimization restarted automatically at the default parameter values, if this
occurs. This will often clear a problem with bad starting values.
19.
Analytic derivatives are implemented for most models since these are faster
than numerical approximation, but the algorithms can fail in certain situations.
In the case of convergence failure from this cause, the iterations are restarted
with numerical derivatives enabled, and a note to this effect appears in the
output. This setting is saved with the model in question. Numerical derivatives
can also be selected manually in Options / Optimization and Run.
GRAPHICS FOR REGIME SWITCHING MODELS
20.
For simple Markov and Hamilton switching models, the M-1 series of
independent filter probabilities can be listed and/or plotted. These are the
probabilities of the regime being occupied conditional on information to
date t, as used to weight the likelihood terms in estimation. In the case
of Hamilton's model, these are summed over lags (p) to reduce M^(p+1)
175
series down to M.
21.
For the explained switching model, the M-1 series of variable switching
probabilities are also plotted. When regime dummies have been specified
there are up to M-1 different series for each regime, although differing
only by the same offset at each t. These are averaged to create the series
plotted.
22.
For the smooth transition model, the regime weights are plotted (logistic
functions of the transition indicator).
BOOTSTRAP AND SUBSAMPLING P-VALUES
23.
Resampling computing p-values for tests by tabulating the statistics for
a "pseudo-true" model, where the statistics are centred using the relevant
components from the sample counterparts. This method can be used for
t-ratios and Wald tests, and also M and CM tests. It is not so easily
implemented for LM tests, although diagnostic tests for i.i.d. residuals
are valid by construction in the bootstrap context. Other LM tests,
and other tests are given their conventional asymptotic p-values. Note
that resampling p-values are always indicated with a '*'.
24.
Resampling p-values are computed for the Jarque-Bera test only for
the bootstrap using Gaussian shocks. Otherwise the hypothesis is true by
construction, so the bootstrap p-values are uninformative.
25.
The cointegration tests (ADF and Phillips-Perron) cannot be resampled
since there is no way to set up a pseudo-true version of the null hypothesis.
Note that in single-equation regression models, the regressors (except
lagged dependent variables) are held fixed in repeated samples. In
cointegration models this is an unrealistic assumption even in large samples.
It is better to consider a multi-equation model in which the unit root
processes are generated endogenously. Monte Carlo experiments can
be used to evaluate inference procedures in this case.
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11 Directories and Files
DIRECTORIES (Windows folders):
Start-in
Must be specified by the operating system when TSM4 starts.
This is usually set by the short-cut used to start the program,
Options are presented by the installation program, or it can
be set manually by editing the short cut. Otherwise, by default
it is the directory where the Ox file used to start the program
resides.
Notes:
1.
On networks or shared systems, the user must have write
permissions in the Start-in directory. Write permissions in the
TSM Home directory ([ox-home]/packages/tsmod4/) are not
required. It is NOT recommended to designate TSM-Home as
the Start-in directory.
2.
In the Windows installation of TSM, double-clicking on a .tsm
file in Windows Explorer starts the program with the settings in
question. The Start-in directory is one where the .tsm file
resides. If the file is selected from a Start Menu the Start-in is
the user's registered home directory.
Results
Selected by the user as an alternate location for program outputs.
By default, it is the same as the Start-in directory. Change the results
folder in one of two ways:
*
By the command File / Results / New Results File ... The
folder containing the chosen file becomes the new results
folder.
*
By the command File / Folders / Results... Browse to the
required path, or type in the text field.
FILES
These files may be created by TSM4 in either the Start-in or Results directory.
(S) indicates that a file can only reside in the Start-in directory. Otherwise, it will
be created in the Results directory if that is different. (C) indicates that these file
names can optionally be changed for a particular installation, by editing the file
tsmgui4.h.
settings.tsm (S,C)
Contains all the user's settings and specifications,
including the most recent estimates, and stored model
specifications. Saved automatically before estimation
or simulation runs, and at closedown.
registration.txt
Contains the user's licence code. By default, this is written
to the TSM Home directory, subject to the user having
write permissions, and there being no pre-existing licence
file there. Otherwise, it is written to Start-in directory or, if
this also contains a licence file, to the current results
folder. This allows multiple licenced users to share the same
installation.
NOTE. The program looks for registration.txt in reverse
177
order, first looking in current Results directory, then in
Start-in if this is different, and finally in TSM Home. The
'registered user' for the current run is therefore the user
who starts the program.
tsmod_run.ox (S,C) User-editable Ox file, used to start the program
incorporating the user's own code. The program
can be started by running this file in OxEdit.
(See Appendix A on changing module settings.)
usercode.ox (S,C)
This is the standard container for user's Ox code,
although it is often convenient to have it contain just
#include "..." compiler directives referring to files of code
supplied by the user.
errchk (S)
Written by TSM4 at startup and deleted at closedown.
Used to signal an error termination.
FILE TYPES
*.tsm
Named settings file with .tsm extension, same format as
settings.tsm, saved by the user. Can be loaded manually
to overwrite existing settings. When created using the
File / Export... option, data and listings are bundled with
the settings. The corresponding files are recreated
automatically when the file is loaded, in this case.
*.tsd
Contain specifications, values, graphs, listings and (optionally)
data associated with models stored using the Model Manager.
The file name is the same name as the model name. The
specifications and values are also stored in the settings (.tsm)
file, and since the other content can typically be recreated
by re-running estimations, they may be treated as temporary.
They will be deleted when the model is deleted, and also at
closedown, if the general option "Delete Temporary files on
Exit" is checked. However, their contents can also be imported
directly, so that models can be passed from one installation or
project to another.
*.txt
The program creates various files in standard text format,
including results files (images of the results window text)
and settings files created with the Settings / Save Text...
command. These files can be view and edited in Windows
Notepad or other word-processing programs.
*.xls, *.xlsx, *.csv
Microsoft Excel spreadsheet format is the default format for
saving data sets, forecasts, and other listings. Other options
available in the Options / Output and Retrieval dialog. *.csv
files are text files, have the same capabilities as the Excel
2 spreadsheets created by Ox, and are widely portable.
*.ox
Text files containing Ox source code. They can be executable,
178
such as tsmod_run.ox, but can also be included in other .ox
files using the compiler directive ' #include "..." '. In normal
use, a user's code files should be "#include"d in the standard
code file usercode.ox. which is in turn #included in the
executable tsmod_run.ox.
*.plt
Graphics file produded by Gnudraw, formatted for input to
Gnuplot. These files are deleted by default after Gnuplot
has processed them, but are optionally saved in the Results
directory for further processing by the user. They are ordinary
text files and can be viewed and edited in Notepad, OxEdit
and similar programs.
*.png
The default bitmap graphics format. This format is read by
a wide range of commercial graphing and word processing
software, and converted to formats such as bitmap, Jpeg,
Tiff, etc.
*.eps
Default vector graphics format. Can be read by various public
domain software, and converted to .wmf, .emf and other
formats by most graphics packages. Can also be inserted
in Microsoft Word documents.
TSM saves data and graphics in a variety of other optional formats. See 2.2 File
/ Data..., 8.1 Options / Output and Retrieval and 8.5 Options / Graphics for
details.
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12. Hints and Tips
Here are some non-obvious pointers for getting the best results from the program.
Suggestions from users for further tips are always welcome.
NUMERICAL OPTIMIZATION
1.
TSM's optimization algorithm uses analytic derivatives, by default, wherever
these have been coded. A few of the less frequently used models including
the GED likelihood, EGARCH, DCC and BEKK GARCH, explained
regime switching and Hamilton's model, still depend on numerical derivatives
in Version 4.31. Analytic derivatives will be coded for these models too, as
time permits. Numerical derivatives can be selected optionally as a backstop,
in case an unforeseen problem is encountered - see Options / Optimization and
Run... The option to use numerical derivatives is saved with a model. The
option is enabled automatically if TSM itself detects any problem with the
coded formulae.
2.
Whatever optimization method is used, success can greatly depend on
the good choice of starting values. Some packages implement elaborate
schemes to choose starting values automatically for specific models, such
as ARIMAs, but this type of strategy is difficult to combine with a wide
range of models. TSM implements a number of basic strategies, but these
cannot entirely replace the user's initiative in exploring the parameter
space to achieve successful optimization.
3.
A limited number of steps using the simulated annealing (SA) algorithm are
optionally taken with a view to getting good starting values for the BFGS
gradient-based algorithm. This option is selected by default, but switching
it off may speed things up if the estimation criteria are well-conditioned.
SA uses randomization to decide on successive steps, and with a multimodal criterion function, it is possible for successive runs of the search
algorithm to converge to different points, from the same initial values.
Running SA for a limited number of steps before starting BFGS has the
effect of randomizing the BFGS initial values. Repeating an optimization
run from different starting points or with different algorithm settings is,
in any case, always a sound strategy.
4.
The program makes a maximum of two attempts to perform an optimization,
where the second attempt uses the default starting values. If both attempts fail,
there are several program settings that may assist.
*
Enable the parameter rescaling option in Options / Optimization
and Run... Set the value to unity to limit the ratio of largest to smallest
parameters (effective only if starting values are a guide to the relative
magnitudes). Setting to a higher value (e.g.10) inflates all parameter
values, to reduce the risk of rounding error in the evaluation of
numerical derivatives.
*
Tinker with the simulated annealing settings in Options / Optimization
and Run... There are not many useful guidelines for good choices here;
180
in most cases raising the number of iterations cannot hurt, but also try
switching it off (see Note 3).
*
The scaling of the variance/intercept parameter in GARCH models
can be critical, especially in the IGARCH case. See Options / ML
and GARCH... for details.
*
Experiment with the settings for EGARCH and GARCH-M models
in Options / ML and Dynamics...
*
For dynamic parameters (AR, MA etc.) experiment with the bounding
option in Options / Optimization and Run...
None of these fixes is guaranteed to improve matters, but setting starting
values to good guesses of the estimates is always helpful. For example, if it
is believed that a unit root exists in ARMA (or GARCH) models, start the
AR parameter at 1, rather than 0. Using the "Impose Unit Root" option in
Model / Dynamic Equation may help similarly.
5.
Another good strategy with a complicated model is to simplify it initially,
by deleting or fixing some components. Estimate the simple model, then
add back the deleted components one at a time. The estimates of the
simpler model often provide the best starting values for those parameters
in the more general one. This 'stepwise' approach to the optimum is often
successful when an attempt to optimize the full model from the default
initial values ends in failure.
6.
As a last resort, try keeping a parameter away from illegal values by
imposing inequality constraints. Set them in Values / ... after checking
the checkbox for Parameter Bounds. This won't work if, for example,
the optimum is actually on the boundary of the feasible region. In this
case, simply fix the parameters in question at the boundary values.
Conventional inference won't be possible on these parameters.
7.
The estimation output can be optionally printed in the event of nonconvergence - but note the caution given on the Options / Optimization
and Run... help page, regarding the interpretation of these reported
values.
8.
Switching regime models (Markov switching and smooth transition
models) generally exhibit multiple maxima of the likelihood. Good
starting values, and careful experimentation with different starting values,
is strongly recommended. As a switching probability tends to 0 or 1,
the likelihood becomes flat due to the logistic mapping employed, and
the algorithm can get stuck at these points. Restarting with "plausible"
probability values (such as 0.9, 0.1 in the 2-regime case) often succeeds
in this situation.
CHOICE OF SYSTEM ESTIMATORS
9.
Don't overlook the distinction between the Linear Regression and Dynamic
Equation options. The latter always uses numerical optimization to compute
181
the estimator, even when a closed-form solution exists. Large unrestricted
VARs may be computed in the Linear Regression dialog using SUR.
Exclusion restrictions can be imposed by "fixing" parameters, although
they can be tested only by Wald tests on the unrestricted model.
10.
There are two procedures to estimate a Gaussian linear equation system
by maximum likelihood. Least generalized variance (LGV) optimizes the
concentrated log-likelihood function (the log-determinant of the
covariance matrix). The "Gaussian ML" option estimates the loglikelihood as a function of all parameters, including the variance matrix,
and hence is much more computationally intensive than LGV. This
method is only required for models with nonlinear features such as
ARCH/GARCH or Markov switching.
USING THE RESULTS WINDOW AS A TEXT EDITOR
11.
Text can be typed or pasted freely into the window. To paste from the
clipboard, right-click in the text area and choose Paste. To save text in a
file, first name the file with File / Results / New Results File. Then select
the desired text with the mouse and give the command File / Results /
Save Selected Text. Note that subsequent saves will be appended to the
same file. To avoid this behaviour, give the New Results File command
again to create or reinstate a results file.
ENTERING DATA BY HAND
12.
Use one of the following methods to type data directly into the program,.
The second method is recommended for entering several variables at once.
Don't forget to save the data set afterwards, before doing anything else.
13.
Use the Setup / Data Transformation and Editing dialog to create a new
variable. If no data are currently loaded, give the command Re-Size Sample
and enter the desired sample size, in which case a new variable Zeros is
created automatically. Otherwise, give the command Make Zeros. Use
Rename to change Zeros to the name of the new variable. Then choose
Edit/List /Compare, select the first observation, and press Edit Observation.
To enter successive observations, type the values into the edit field and
press "Enter", repeatedly.
14.
A sequence of observations on a variable can also be pasted into TSM
using the Windows clipboard. The values can be columns in a spreadsheet,
or typed into a text editor or word processor. In the latter case, spaces,
tabs, commas and carriage returns can all be used as separators.
To copy the text in the source application, the usual routine is to
highlight it, then right-click and choose 'Copy' from the context menu, or
issue the keyboard command Ctrl-C. Then open the List/Edit dialog as
above, select the first cell in the target range, and either press "Paste
Clipboard" or give the keyboard command Ctrl-V. If the data have been
typed in a text file by variable with observations in columns (spreadsheet
format), read the file into OxEdit and select a single column using the
right mouse button.
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15.
The last paragraph describes a feature implemented only in the Windows
version of TSM. An alternative procedure is to load a text file directly.
In this case, type the data as a matrix with observations in rows and
variables in columns, spreadsheet style, either into a text editor
or into the results window as described in 11 above. The first line should
contain two integers: the number of observations (= lines to follow the first)
and the number of variables (= values on each line). Separate entries on a
line with a space, and terminate each line with [Enter]. Save the file with
extension .mat or .txt. Next, select either File / Data / Open or File / Data
/ Merge, as appropriate. The new variable(s) are named Var# by default,
where # denotes the column number(s). Give new names using 'Rename',
and optionally enter descriptions using 'Description' in the Setup / Data
Transformation and Editing dialog. Before doing anything else, save the
data in text or a spreadsheet format.
MAINTAINING AND EXPORTING PROGRAM SETTINGS
16.
To save a model specification, including data file name, estimator, sample
size, parameter values, test options, etc., open the Model Manager
('double-M' button) select 'Store Current Model' and supply a name
(the current run number is the default). This facility allows you to work
on different projects in parallel during a session. You may have a
complex multi-equation model set up, and need to do some exploratory
regressions or swap data sets. Saving the model allows you to reload the
settings later, using the 'Load Model' command in the Model Manager.
Your stored models are saved with the other settings in the settings.tsm file.
17.
To keep a permanent copy of your favourite operational settings, save
them in a backup file with a name such as "mydefaults.tsm". If you then
need to change the settings for a particular run, they are easily restored by
the command File / Settings / Open, and selecting the backup file. (Note
that restoring settings does not reset the run ID counter.)
18.
Named settings files are also useful in a teaching context. Students can be
supplied with a ".tsm" file containing a desired set of defaults and also
stored models for estimation or simulation exercises. The students can
easily undo any changes they have made by reloading the defaults file.
19.
By default, settings files are saved with local path information to locate
data and listings files, which may make them unsuitable for transfer from
one installation to another. Use the "Export" option in File / Settings /
Save As... to omit this local information. The search path for all files
will then be set to the "Start-in" directory when the settings file is loaded.
In addition, the currently loaded data sets and model outputs (.tsd files)
are bundled in the exported file, and unbundled to the "Start-in" directory
when the file is subsequently loaded. For example, a class exercise
with preset model specifications and data can be distributed to students
in a single exported ".tsm" file.
20.
To over-ride the default behaviour of setting the run ID number to zero in a
new settings file, go to Options / General / Special Settings and enter the
desired number under "Initialize Run ID". This number will be instated at
183
the next estimation run. Alternatively, add the line " RUN_ID = ***; "
to a text file of settings before loading them as described in Appendix E.
DOING SIMULATIONS
21.
A star feature of the program is the ability to stochastically simulate any
model that it can estimate, using either randomly resampled residuals or
computer-generated shocks. The simulation module is the basis for
nonlinear forecasting, bootstrap testing, and Monte Carlo experiments.
To gain insight into the properties of an estimator, it is always a helpful
exercise to apply it to artificial data from a known model.
22.
To create an artificial sample, do the following
1)
Clear the data (File / Data / Clear).
2)
Set a sample size. In Setup / Data Transformation and Editing,
choose Edit, scroll down to 'Re-Size Sample', enter a value, and
press 'Go'. A variable called Zeros with the specified number of
observations is automatically created.
3)
Open Options / Simulation and Resampling, and choose a shock
distribution, either Gaussian or Model. In the first case, also set
the shock variance. In the second case, a likelihood function
must be specified in Model / Dynamic Equation.
4)
Set the model specifications in the usual way, selecting Zeros as the
dependent variable. Pre-sample values are used to start a dynamic
simulation and, if desired, these can be inserted in Zeros in Setup /
Data Transformation and Editing.
5)
Enter parameter values in the relevant Values dialogs. (Don't forget
variance parameters in the case of 'Model' shocks.)
6)
Open the Model Manager and save your specifications under a
suitable name.
7)
Select Actions / Simulate Current Model, and add the artificial data
to the data set if desired.
8)
Alternatively, use your model to set up a Monte Carlo experiment.
Note how a different model can be used to estimate from the
simulated data, to permit misspecification analysis.
23.
Whilst the simulation code has been carefully checked, there are so many
combinations of model features available that it is not possible to guarantee
that they will all work together as intended. To ensure the integrity of
simulation results, it is a good idea to run a check on the selected model.
Users may also wish to check out their own supplied code.
To verify that a model is being correctly simulated, follow these steps:
1)
Evaluate the model with a data set and chosen or estimated
parameters, to generate a set of residuals.
2)
Open Options / Simulation and Resampling, and select 'Bootstrap'
for the Shock Distribution. In the box Random Number Seed, enter
the value -1. This setting causes the simulation to be done with the
actual residuals, without random resampling.
3)
Run Actions / Simulate Current Model and save the simulation. This
should match the original series exactly apart, conceivably, from small
rounding errors. Compare the series in Setup / Data Transformation
and Editing. Choose 'Mark' for one series, then 'List/Edit/Compare' for
184
the other to see them side by side.
In a Markov switching model, the simulation involves random regime
switches. To disable these, put the switching probabilities to 0 or 1 in
the simulation. In the case of explained switching models, choose
parameter values large enough to ensure that the switching
probabilities are either 0 or 1 for nearly all values of the explaining
variables.
Don't forget to reset the random number seed afterwards! Should a flaw in the
simulation code be suspected, please notify the author.
4)
STARTING TSM FROM WINDOWS EXPLORER
24.
Double-clicking on a TSM settings file, with extension ".tsm" and red
TSM icon has the same effect as starting the program from the Start
menu and then loading the settings with the command "File / Settings /
Open...". The "Start-in" directory is in this case the directory where the
target TSM file resides.
25.
Any data file having a supported format can be selected in Explorer and
loaded into TSM. In this case, right-click the file with the mouse and
select the option "Open with ..." from the context menu. Select the
"Choose Program..." option, and choose "start_tsm" (with the Windows
batch file icon) from the list.
If this option does not appear in the list, choose "Browse...", navigate to
the TSM_HOME directory and select the file "start_tsm.bat" from the file
list. It should only be necessary to do this once.
Notes:
1)
If the option "Always use the selected program to open this kind
of file" is checked, simply double-clicking on the file icon will in
future load the file into TSM. Only choose this option if you
don't edit this type of file in your spreadsheet program by default..
2)
The directory containing the data file is used as the Start-in
directory. If it contains a "settings.tsm" file, the settings are
loaded from there. Otherwise, the defaults are set and a new
"settings.tsm" is created.
RUNNING SEVERAL INSTANCES OF TSM
26.
To run lengthy optimizations or Monte Carlo runs, without tying up the
program interface, try the option for exporting batch jobs to be run from
the command line. For details, see BATCH JOBS under 6.1 Actions /
Run Estimation and RUNNING AN EXTERNAL PROCESS under
3.10 Setup / Monte Carlo Experiments. When these jobs terminate, their
outputs are written to text files with the run number. Give the command
File / Load Text File to write the contents to the results window in the
usual way.
27
By default, a batch job is launched automatically to run concurrently
with the GUI. This is the efficient way to make use of a dual core processor,
since TSM is not multi-threaded even under Ox 5. Alternatively the run
(or runs) can be postponed to a time when the machine is otherwise idle.
In this case they must be launched manually, as regular Ox programs.
185
28.
It is also possible to run two or more instances of the GUI concurrently.
The only major problem to be avoided in this case is the different sessions
interfering with each other, by attempting to access and write to the same
files. The trick is to create a different working directory for each instance.
In Windows, do as follows:
*
Use the ' File / Settings / Export ' command to bundle your data
and models into a portable '.tsm' file.
*
Create a new directory for each instance, and copy the .tsm file to
each.
*
Start each instance by double-clicking on the .tsm file (see 23
above).
The directory containing the .tsm file becomes the Start-up directory for
each instance, with data, graphics, '.tsd' (model) and results files all
written there by default.
29.
For a more permanent multi-tasking setup, create multiple Windows shortcuts
on the Start Menu, each edited to point to a different 'Start-In' directory.
Give these shortcuts suitable names to distinguish them.
30.
Another use for multiple instances is where TSM is running the user's Ox
code. The supplied Windows shortcut "TSM4 with User Code" provides
an example. See Appendix C for further details.
TROUBLESHOOTING
31.
If the program appears to behave unpredictably, this may be because a
setting has been changed inadvertently. For example:
*
The values of certain estimated parameters (e.g. MA parameters,
GARCH parameters can depend on program settings.
*
If a parameter is "fixed" at zero in the Values dialog, no value is
reported for it in the output. It might appear that the estimated
specification is different from the chosen one. (Note that when
variable(s) are fixed, the relevant Values button is highlighted and
menu item(s) checked, as a reminder.
*
Corruption of the settings file (which is reloaded at start-up unless
renewed) can occasionally occur.
If you cannot figure out what the problem is, reset the program to
defaults with File / Settings / New. Alternatively, close the program,
delete the "settings.tsm" file, and restart.
32.
Another option is to write the current settings to a text file (File / Settings
/ Save Text...) and inspect this output. Note that only non-default settings
are listed. The usage of variable names can be checked in the programming
manual.
33.
If the program attempts to execute an illegal Ox instruction and crashes,
a message is displayed, and then it automatically restarts. The Ox error
message appears in the console window (second TSM icon on the taskbar)
and can be copied to the clipboard and saved (follow the onscreen
instructions). This message can guide users in debugging supplied code.
If the error is due to a TSM bug, please send in the error message as
186
requested!
34.
The error recovery screen displays options for quitting, continuing, and
exporting the current settings to a file. This file contains valuable diagnostic
information, preserving the last recorded state of the program before the
crash. If possible, please send in this file along with the error message.
35.
Although Ox should read spreadsheet files such as the Excel .xls format
(and .xlsx files with Ox 6.2) it is occasionally found that such files contain
incompatible features. The message "Data input failed" appears. In this
event, use Excel to save the file in comma delimited (.csv) format. These
files are always readable and contain all the information relevant to TSM
functionality. If TSM is then used to save the data in .xls or .xlsx format,
the file will be readable by both TSM and Excel.
187
What's New?
TSM 4.43
*
*
New stochastic simulation feature allows shocks to be constructed by a
formula with standard normal and uniform drawings.
New functions available for calling from an Ox program.
TSM 4.42
*
*
Spreadsheet editing feature, allows editing of raw data files containing
guide columns with dates, date labels, indicators or panel data information
and hidden from the user in normal operations.
Change to the EGARCH specification, subtraction of absolute shock mean
according to the likelihood model (optionally reversible, see Options /
General / Special Settings).
TSM 4.41
*
*
*
*
Stable (infinite variance) shocks can now be generated for use in Monte Carlo
experiments.
The sieve-AR bootstrap technique for dependent data can now be combined
with any bootstrap variant.
New bootstrap option "m/T", to set the bootstrap sample size (m) as a fraction
of the data sample (T).
2-sided option for p-value EDFs in Monte Carlo experiments.
TSM 4.40
*
64-bit compilation released, to run with the 64-bit version of Ox 7.
TSM 4.39
*
*
*
*
“Warp speed Monte Carlo” option for experiments on bootstrap estimation.
Any data transformation can be performed "on the fly" when estimating
a model. One-to-one invertible transformations allow forecasts and
fitted values to be reported for the data in original form.
Nielsen-Jensen (2013) FFT algorithm for fractional differencing implemented.
Runs under Ox Version 7.
TSM 4.38
*
*
*
*
New forecasting code produces analytic forecasts for a wider class of models.
Forecast error variance decompositions for dynamic multi-equation models.
Graphics titles can be either removed or changed by the user.
Automatic data transformations: variables can be arbitrarily transformed on
the fly before estimating a model. If the transformation is 1-1 and invertible,
forecasts from the model can be computed for the original series.
TSM 4.37
*
*
EMF graphics format implemented.
Changes to the forecasting options, the model description format and
regime switching options.
188
TSM 4.36
*
*
*
*
*
Andrews (1993) structural change test.
Consistent specification tests.
V/S test of short memory.
Interface improvements including sorted model lists and Quick Model
Save option.
Principal components and cubic spline data transformation options.
TSM 4.35
*
*
*
State space modelling (requires installation of SsfPack 2.2).
Series plotting with confidence bands.
Improved design of Options / Graphics with Line Styles dialog.
TSM 4.34
*
*
*
Cusum of squares test.
Stationary bootstrap option, static bootstrap option.
Interface improvements:
Values dialogs, list selection, data spreadsheet and data formula menu
commands, multiple dataset handling, resizable data spreadsheet.
TSM 4.33
*
Read/write support for Excel 2007/2010 “.xlsx” data files with Ox 6.20.
TSM 4.32
*
*
*
*
*
*
Programmable graphics functions.
New data-plotting feature allows correlogram, spectrum and QQ plots
of two or more variables to appear in one graph.
Selectable graphics text size, selectable font for exported graphics.
'Logarithmic model' option without prior transformations.
Assignable toolbar buttons increased from two to six.
Enhanced data entry and editing options, with pasting from the clipboard.
TSM 4.31
*
*
*
*
Engle-Rothenberg-Stock tests of I(1).
Robinson-Lobato test of I(0)
Partial autocorrelations can be listed and plotted.
Improved interface, model feature activation
TSM 4.30
*
*
*
*
*
Function optimization using analytic derivatives, implemented for most
models and estimators.
Support for parallel computing using Condor HTC on a network.
Improved forecast fan charts.
Improved dialog design for Tests and Diagnostics.
Ordered probit and logit modelling.
189
TSM 4.29
*
*
*
*
Supports file loading by “drag-and-drop”.
Quick links from the Model menu to load and save
functions for stored models .
Irregular panels supported.
White heteroscedasticity test.
TSM 4.28
*
*
*
Work with multiple data sets in memory.
Monte Carlo parallel processing option.
Filter missing observations in sample selection.
TSM 4.27
*
*
New GUI interface using Java 'Swing', with user-selectable
'look and feel'.
Data viewing and editing in a spreadsheet-format window.
TSM 4.26
*
*
*
*
*
*
*
Panel data estimation for fixed effects models (OLS, SUR, IV, 3SLS)
and single-equation random effects (GLS and ML).
Improved graphing of confidence bands for forecasts and recursive
estimation.
Bierens' conditional moment test of functional form.
New coded model option for simulations: nonlinear shocks.
Data bootstrap, and sample selection by indicators.
Hodrick-Prescott filter.
Bivariate density plots.
TSM 4.25
*
Bootstrap test of I(0).
*
'RGB' scatter plots, with observation dates colour-coded.
*
Improved Monte Carlo output format and EDF handling.
NOTE: further revision of EDF file format!
*
New data editing/transformation options.
*
Improved sample selection options.
*
Consolidates a large number of small modifications and fixes
TSM 4.24
*
Improved facilities for running and sharing Ox code. Code files now
bundled with exported settings, and viewable from the Help menu.
*
EDF files for tabulations of different sample sized can now be merged.
p-values are generated by interpolating the tabulations according to
actual sample size.
NOTE: EDF file and Ox function formats are changed in 4.24!
Files created with and for previous versions of TSM must be modified.
*
External batch processing option for estimation and Monte Carlo runs
- allows multi-tasking and avoids tying up the GUI for long jobs.
*
Improved plotting controls: legends and boxes.
190
TSM 4.23
*
*
Plug-in bandwidth selection and pre-whitening for HAC
covariance estimation.
New graphics options, including forecast fan charts, selectable
line widths, and 8 selectable line style options for series plotting.
TSM 4.22
*
Kiefer-Vogelsang-Bunzel (KVB) inference with inconsistent
covariance matrix estimation.
TSM 4.21
*
*
*
*
*
Nonlinear moving average (SPS) model feature, providing
close approximations to STOPBREAK and STIMA models.
Recursive coded equations can include the lagged value as
an argument.
Extended options for coding nonlinear models, including
nonlinear ECMs, and nonlinear MAs using the recursion
feature.
Panel to create/edit/view a model description. Text is saved
with the model.
Forecast confidence bands now plotted in system forecasts.
System impulse response option.
TSM 4.20
*
*
*
*
*
*
*
Automatic regressor selection by optimizing info. criterion.
Local Whittle ML long memory estimation.
Coded (nonlinear) equilibrium relations.
Supplied EDF option for critical values extended to Ox-coded
test statistics.
Text files can be loaded into the results window for editing.
"Restart" option, for one-click incorporation of changes to user's
Ox code.
Randomized coded simulation models.
TSM 4.19
*
*
*
*
*
A formula parser enables three new features:
o
Algebraic data transformations.
o
Nonlinear parameter restrictions (replaces existing procedure).
o
Nonlinear equation estimation - complements the existing ability to
compile Ox functions into the program. More limited in scope, but
much simpler to implement.
Save and use tabulations of test EDFs. This feature implements size
correction and estimation of true test powers in simulation experiments.
Can also be used to make bespoke tabulations of non-standard tests.
"Save Selected" command - write selected variables from data set to new
file.
Harris-McCabe-Leybourne (HML) test for long memory of data/residuals.
Two assignable toolbar buttons, + other interface improvements.
191
*
*
*
Improved implementation of supplied Ox-coded statistics.
Fourier bootstrap option.
Nyblom-Hansen model stability tests.
TSM 4.18
Code recompiled under Ox 4.02. Dedicated "Stop" button on toolbar to pause
calculations. Data plots can be displayed directly, by clicking the variable list in any
dialog, and then the "Chart" button. Excel dates for weekly and daily data are read
with the data, and used in the output and plots.
TSM 4.17
Progress indicator for numerical optimizations shows the number of
iterations and current criterion value.
Improved code for setting model specifications. Parameter values and settings
are now preserved under deletion/restoration of regressors. In systems,
equations can be deleted/restored without losing values and settings.
Enhanced Monte Carlo module allows multiple experiments in a single run,
Experiments can also be extended with additional replications.
'User-supplied statistic' option allows the Monte Carlo module to have a fully
general application. The distribution of any function of the data set, coded by the
user in Ox, can be studied by simulation, after using TSM's modelling facilities
(or user-supplied code) to generate the data.
TSM 4.16
In the Windows installation, the program can now be started by simply clicking
on a ".tsm" (settings) file in Windows Explorer. These files are identified by the
TSM icon, as for the Start Menu shortcuts.
A new File / Import Models... function allows model specifications to be copied
from one settings file to another.
The File / Export... command is enhanced to save the data and listings files as
part of the ".tsm" file. A single settings file can now record a complete working
environment, including data, models, graphs and parameter values, and be
opened by a single keystroke on a different installation. When an exported file
is opened, the data and listing files are recreated automatically in the Start-in
directory.
Additional resampling options – sieve-AR bootstrap.
Scatter plots now show regression lines superimposed.
TSM 4.15
has a redesigned interface. Here are the main changes from Versions 4.14 and
earlier.
*
The Estimation and Sample dialog has been replaced with a simplified
Set Sample dialog. This no longer has a toolbar button, but is
accessible as a floating window in all the model specification
dialogs.
*
Estimator selection buttons and 'System of Equations' checkboxes
are now located as appropriate in the redesigned Linear Regression
192
and Dynamic Equation dialogs.
*
A Parameter Bounds / Grid-Plotting checkbox is located in each
Values dialog. The Minimand option is selectable in Options /
Optimization and Run.
*
Kernel selection for HAC estimators has been moved from Options /
General to a redesigned Options / Tests and Diagnostics dialog.
*
The Options / Bootstrap and Simulation dialog is now renamed as
Simulation and Resampling, and controls both bootstrap and the
new subsampling options.
*
The new "Dialog" toolbar button can be used in two ways. By default
it re-opens the last dialog closed, excepting dialogs with their own
buttons. Hover the mouse over it to see its current assignment.
Alternatively, it can be permanently assigned to one of a range of
dialogs normally accessible from the menus. Set your choice in
Options / General.
193

User’s Manual Time Series Modelling Version 4.43 James Davidson

Transcription

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